:salamext:
I think this is explained in the tafsir/explanation of the verses;
(Who is he that can intercede with Him except with His permission) is similar to His statements,
[وَكَمْ مِّن مَّلَكٍ فِى السَّمَـوَتِ لاَ تُغْنِى شَفَـعَتُهُمْ شَيْئاً إِلاَّ مِن بَعْدِ أَن يَأْذَنَ اللَّهُ لِمَن يَشَآءُ وَيَرْضَى ]
(And there are many angels in the heavens, whose intercession
will avail nothing except after Allah has given leave for whom He wills and is pleased with) [53:26], and,
[وَلاَ يَشْفَعُونَ إِلاَّ لِمَنِ ارْتَضَى]
(They cannot intercede except for him with whom He is pleased) [21:28].
These Ayat assert Allah's greatness, pride, and grace, and that no one dares to intercede with Him on behalf of anyone else, except by His permission. Indeed, the Hadith about the intercession, states that the Prophet said,
«آتِي تَحْتَ الْعَرْشِ فَأَخِرُّ سَاجِدًا، فَيَدَعُنِي مَا شَاءَ اللهُ أَنْ يَدَعَنِي. ثُمَّ يُقَالُ: ارْفَعْ رَأْسَكَ، وَقُلْ تُسْمَعْ، وَاشْفَعْ تُشَفَّعْ قَالَ: فَيَحُدُّ لِي حَدًّا فَأُدْخِلُهُمُ الْجَنَّة»
(I will stand under the Throne and fall in prostration, and Allah will allow me to remain in that position as much as He wills. I will thereafter be told, "Raise your head, speak and you will be heard, intercede and your intercession will be accepted''. The Prophet then said, "He will allow me a proportion whom I will enter into Paradise.'')
SOURCE
The issue of intercession is in regard to the hereafter i.e. on the Day of Judgement, the Prophets, and the righteous will be able to intercede on behalf of others, only when Allaah permits. So on the Day of Judgement, there will be sinful Muslims who will have been punished in the hellfire. But a believer does not remain in the hellfire forever [this is only for those who died in a state of kufr/disbelief], rather the punishment of the hellfire is a form of expiation for his/her sins. So the Messenger of Allaah (peace be upon him) will intercede for these people on that day, that Allaah may remove the sinner Muslims out of the fire.
Indeed, both Sahih Muslim and Sahih Bukhari relate that the Prophet (peace be upon him) said: "Every prophet is allowed one answered prayer. As for me, I delayed my request in order to intercede for my community on Judgment Day."
There are other narrations also of a Shaheed (one who has been killed while fighting in the cause of Allaah) will be able to intercede for 70 muslim family members who may have been liable to the punishment of the hellfire. There are also ahadith of the haafidh of Qur'an (one who memorizes Qur'an), and them having the permission to intercede on behalf of 10 Muslim family members on the Day of Judgement. Yet none of these people will be able to intercede for these people (i.e. beg Allaah to remove these people from His punishment) except until He permits.
So the intercession isn't in regard to this life, rather it is in regard to the hereafter on the Day of Judgement. And Allaah knows best.