Actually, their leading scholars and missionaries acknowledge the conversion rates to Islam.
Joel Richardson, a Christian Missionary, clarifies in his book against Islam entitled
The Islamic Revival
The clearest reason to study and understand Islam and specifically Islamic eschatology is quite simply because Islam is the future. Yes, you read that correctly: Islam is
the future. If present trends do not change dramatically
, Islam will bypass Christianity for the title of the world’s largest religion very shortly. In fact, according to most statistics, this may take place in less than twenty years. A majority who read this book will live to see this. Islam is the fastest growing religion in the world, growing at a rate four times faster than Christianity.  Presently those who practice Islam make up approximately one fifth of the world’s population. One seasoned Bible teacher from England after reviewing the statistics recently commented that, “if present trends continue, half of all global births will be in Muslim families by the year 2055”.  Something dramatic and revolutionary is happening right before our eyes, and most western Christians are oblivious to it. The purpose of this chapter is to inform the reader about the rapid growth of Islam. The picture that is about to be painted may surprise some people. Some may be confused. Some may even deny it, but it is the truth and it needs to be told. Even by itself, the growth and spread of Islam is a powerful wake up call to all Christians.
Not only is Islam the fasting growing religion in the world, but also in the United States, Canada and Europe.  The annual growth rate of Islam in the US is approximately 4%, but there are also strong reasons to believe that it may have risen to as high as 8% over the past few years. Every year, tens of thousands of Americans convert to Islam. Prior to 2001 most reports seem to have the number roughly around 25,000 American converts per year.  This may not sound like that much, but this yearly figure according to some Muslim American clerics has quadrupled since 9-11.  Since 9-11 the numbers of American converts to Islam has skyrocketed. As early as one month after the World Trade Center attacks, the reports were flowing in from Mosques all over America. Ala Bayumi, the Director of Arab affairs at the Council for American Islamic Relations (CAIR) on November 11, 2001, in the London daily newspaper, Al-Hayat
Non-Muslim Americans are now interested in getting to know Islam. There are a number of signs... Libraries have run out of books on Islam... English translations of the Koran head the American best-seller list... The Americans are showing increasing willingness to convert to Islam since September 11... Thousands of non-Muslim Americans have responded to invitations to visit mosques, resembling the waves of the sea crashing on the shore one after another...
After testifying to the dramatic strides that Islam had taken as a result of the 9-11 attacks, Bayumi goes on to say that:
Proselytizing in the name of Allah has not been undermined, and has not been set back 50 years, as we thought in the first days after September 11. On the contrary, the 11 days that have passed are like 11 years in the history of proselytizing in the name of Allah. 
In an article from the British newspaper, The Times of London
, January 7, 2002 just four months after 9-11 we read:
There is compelling anecdotal evidence of a surge in conversions to Islam since September 11, not just in Britain, but across Europe and America. One Dutch Islamic centre claims a tenfold increase, while the New Muslims Project, based in Leicester, [England] and run by a former Irish Roman Catholic housewife, reports a “steady stream” of new converts. 
And at the time of this writing in late 2004, this phenomenon does not seem to be waning. I recently asked a Muslim acquaintance how many Americans he has witnessed convert to Islam in just the past year. He explained that he has personally participated in at least one hundred conversion ceremonies in the past year alone. I have similarly asked dozens of American Muslims if they have witnessed a dramatic increase in conversions to Islam since 9-11 and the answer every time has been a resounding yes
. Newer official data is difficult to come by and analyze for more than one reason. First of all, very few comprehensive studies have been done since 9-11; most studies seem to have been done just prior to 2001. Also, since 9-11, many American Muslims are very hesitant to give information away to pollsters who come to the Mosques. There is a widespread suspicion among the Muslim community that pollsters are merely gathering information for the United States Homeland Security Administration or the FBI. Most converts wish to remain relatively anonymous. But from my own personal, albeit anecdotal, experiences, I have talked to many American converts to Islam who have converted since 9-11.
But here’s the other sad [sic!] aspect of these figures: Over 80% of these American converts to Islam were raised in a Christian Church.  If the higher figures of conversion are accurate, that would mean that as many as 60,000 Americans, who were raised in Christian homes, are converting to Islam annually. I have one acquaintance who, although he was a pastors son raised in a deeply religious and traditional Christian family, nevertheless converted to Islam in college. I have read numerous testimonies of priests, missionaries, divinity students, and normal everyday Christians who have converted to Islam. Some are even self-described former “spirit filled Christians”. Some may object that this is impossible. If this is the case, some might object, then why aren’t these statistics more widely known? You may be wondering why you do not personally know anyone who has converted. There are easy answers to these questions. One of the primary reasons that these trends have gone largely unnoticed is that most American Muslims are concentrated in the larger metropolitan centers. The greater Chicago metropolitan area for instance is home to well over 350,000 Muslims. Greater New York City has twice that with over 700,000 Muslims.  The other important statistic that sheds light on why this issue isn’t more commonly discussed in many white American churches is sadly because 85% of American converts to Islam are African-American. White Christian America has not nearly been as impacted by this phenomenon as African-Americans have. It is a very sad commentary on the discontinuity and disunity of the American Church. Islam is absolutely sweeping through the inner cities. One Muslim authority estimates that by the year 2020 most American urban centers will be predominantly Muslim.  But as the number of conversions increases, the face of the Muslim convert is changing as well. Shortly after 9-11, National Public Radio did a special on Islam and those who had converted after 9-11:
One of the most important topics [in an NPR broadcast] was an interview with several young women at American universities who recently converted to Islam through the Islamic Society of Boston. They hold advanced degrees from universities in Boston, such as Harvard, and they spoke of the power and the greatness of Islam, of the elevated status of women in Islam, and of why they converted to Islam. The program was broadcast several times across the entire U.S...
From an article in The New York Times, October 22, 2001, we read a portion of Jim Hackings story:
Nine years ago, Jim Hacking was in training to be a Jesuit priest. Now, he is an admiralty lawyer in St. Louis who has spent much of the last month explaining Islam at interfaith gatherings… He made the Shahadah [Muslim Conversion ceremony] on June 6, 1998. "The thing I've always latched to is that there's one God, he doesn't have equals, he doesn't need a son to come do his work," (emphasis mine) 
A typical testimony of a former Christian convert reads:
As a child, Jennifer Harrell attended church and Sunday school. In high school, she was on the drill team and dated a football player. After college, she became a Methodist youth minister. At age 23, she became a single parent. At age 26, she became a Muslim. "I grew up in Plano doing all the things I thought I was supposed to do," said Ms. Harrell, 29, of Dallas. "I went to church. I went to parties. But I wasn't concerned about heaven or hell. I took it all for granted." Eventually, she took a job in sales, where she was introduced to Islam by Muslim co-workers. One of them loved to debate religion, which stirred Ms. Harrell to rethink her Christian faith. She studied the Bible, but also Islam in order to do a better job of defending her faith. Instead, she became intrigued that Muslims prayed five times a day, fasted and gave alms as a way of life. "I wasn't the type of Christian who prayed every morning," she said. She said Muslim beliefs about Jesus made more sense to her because they revere him as a prophet and not God's son. "When I was a Christian, I never understood why Jesus had to die for my sins," Ms. Harrell said. "I mean, they're my sins." Before becoming a Muslim, she visited a Christian minister. She said she asked why Christians ate pork, why women didn't cover their heads in church, and why Christians dated. "I wanted him to defend the Bible," she said. "I gave him everything that I had found wrong with Christian interpretation." His answers didn't satisfy her.
Stories like Jim Hacking’s and Jennifer Harrell’s are legion. I have probably read a hundred such stories.
...For now, the point that needs to be emphasized is that the beliefs of the world’s second largest and fastest growing religion should matter to us
. This is especially true in light of Islam’s potential to soon become the world’s largest religion. A fair prediction is that if the time comes when Islam indeed does bypass Christianity as the world’s largest religion, or even as it merely begins to draw closer to that point, there will be a tipping point whereby the rate of growth will increase exponentially. Bandwagon conversions and confusion among faithful Christians will be the rule of the day. We cannot underestimate the power of a worldwide trend. Indeed one of the primary aspects of the last-days is what the Bible calls the “great apostasy,” which will be a significant global falling away from the Christian faith. While Islam now exists as an insecure religion wrestling with why Allah has allowed Islam to remain an inferior presence in the earth compared to Christianity, the days will likewise come for Christians, when they too will have to wrestle will why God has allowed Islam to bypass Christianity in terms of both growth and influence. This could begin to happen as soon as fifteen years from now. It could be sooner. I sincerely hope that this is not the case, but at present, there are very little indicators to suggest otherwise. The only hope for a turnaround in this trend would be a significant full-scale worldwide revival; the kind of revival that until now has never been seen. But for now, as the trend is just beginning in America, it is time to become informed and prepared for what promises to be the Church’s greatest challenge ever. As I said earlier, Islam is the future (albeit only temporarily so). It is time for the Church to face reality. As Brother Andrew, the man who became so well known for smuggling bibles past the iron curtain, as told in the modern Christian classic, God’s Smuggler
, said as early as 1994, “What Communism was to the twentieth century, Islam will be for the next one hundred years.” 
1. David Pawson, The Challenge of Islam to Christians (London, Hodder and Stoughton, 2003), p. 11
3. Bruce a. Mcdowell and Anees Zaka, Muslims and Christians at The Table (Phillipsburg, P& R Publishing, 1999), p. 6
5. New York Times, October 22, 2001, Jodi Wilgoren, Islam Attracts Converts by the Thousands, Drawn Before and After Attacks,
6. Al-Hayam Newspaper (London), November 12, 2001, as quoted in Middle East Media & Research Institute, November 16, 2001, Muslim American Leaders: A Wave of Conversion to Islam in the U.S. Following September 11
7. Al-Ahram Al-Arabi (Egypt), October 20, 2001, as quoted in Middle East Media & Research Institute, November 16, 2001, Muslim American Leaders: A Wave of Conversion to Islam in the U.S. Following September 11
8. The Times, (UK) January 7 2002, Giles Whittell, Allah Came Knocking At My Heart
9. Mcdowell, Zaka, p. 6
10. ibid. p. 6
11. ibid. p. 7
12. Middle East Media & Research Institute, November 16, 2001, Muslim American Leaders: A Wave of Conversion to Islam in the U.S. Following September 11
13. New York Times, October 22, 2001, Jodi Wilgoren, Islam Attracts Converts by the Thousands, Drawn Before and After Attacks
14. The Dallas Morning News – November 3, 2001, Susan Hogan,
19. Brother Andrew, Light Force, (Grand Rapids, Fleming H. Revell, 2004), p.140