1. There are different sorts of du'as. As Bediuzzaman Said Nursi puts it, it is either through the tongue of innate ability like the supplication of plants and animals, through which they seek forms from the Absolute Bestower and to display and manifest His Names. Or it is through the tongue of innate need. These are the supplications for all their essential needs – beyond their power to obtain – offered by animate beings. Through this tongue, the animate beings seek certain things from the Absolutely Generous One for the continuance of their lives, like a sort of sustenance. Or it is supplication through the tongue of exigency, through which all beings with spirits who find themselves in some plight or predicament make supplication and seek urgent refuge with an unknown protector; indeed, they turn to the All-Compassionate Sustainer. If there is nothing to prevent it, these three sorts of supplication are always accepted.
The fourth sort of supplication is the most well-known; it is our supplication. This too is of two sorts: one is active and by disposition, and the other,verbal and with the heart. For example, having recourse to causes is an active prayer. To gather together causes is not in order to create the effect, but through the tongue of disposition to take up an acceptable position in order to seek the effect from Almighty God. To plough a field is to knock at the door of the treasury of mercy. Since this sort of active supplication is directed towards the Absolutely Generous One’s Name and title, it is accepted in the great majority of cases.
The second sort is to offer supplication with the tongue and the heart. It is to seek certain wishes which the hand cannot reach. The most important aspect, the most beautiful aim, the sweetest fruit of this is this: “The one who offers the supplications knows that there is Someone Who hears the wishes of his heart, Whose hand can reach all things, Who can bring about each of his desires, Who takes pity on his impotence, and answers his poverty.”
2. There is a difference between answering a du'a and accepting it. Allah (s.w.t.) says in the Qur'an "Call upon Me and I will answer you (40:60)".
If you say: We frequently offer supplications, but they are not accepted. But the verse is general, it states that every supplication is answered.
The Answer: To answer is one thing, to accept is something quite different. Every supplication is answered, but its being accepted and exactly what was sought being given is dependent on Almighty God’s wisdom. For example, if a sick child calls the doctor, saying: “Doctor! Doctor!”, and he replies: “Here I am, what do you want?”, and the child says: “Give me that medicine!”, the doctor will either give him exactly what he asks for or something better and more beneficial for him. Or knowing that medicine is harmful for his illness, he will give him nothing.
Thus, since Almighty God is all-present and all-seeing, He responds to the supplications of His servants. Through His presence and response, He transforms the desolation of loneliness and solitude into familiarity. But He does this, not in accordance with man’s capricious and importunate demands, but in accordance with the requirements of dominical wisdom; He gives either what is sought or what is better than it, or He gives nothing at all.
For example, someone asks for a son and Almighty God bestows a daughter like Mary. One should not say that his supplication was not accepted, but that it was accepted in a better way.
Also, sometimes a person makes supplication for his happiness in this world and it is accepted for the hereafter. One should not say that his supplication was rejected, but that it was accepted in a better form. Similarly, Almighty God is All-Wise; we seek from Him and He responds to us. But He deals with us in accordance with His wisdom.