Are all the Prayers of Prophets accepted?

The Anti-Ahmadis allege that a certain prayer of the Promised Messiah (AS) was not accepted, thus, he is a false prophet. In their enmity of Ahmadiyya Islam, they blaspheme many prophets including the Prophet Muhammad (SAW) and declare them false prophets as well. Nauzubillah!

Just a couple of ahadith that are enough to expose the blasphemy of the Anti-Ahmadis:

سَأَلْتُ رَبِّي ثَلاَثًا فَأَعْطَانِي ثِنْتَيْنِ وَمَنَعَنِي وَاحِدَةً سَأَلْتُ رَبِّي أَنْ لاَ يُهْلِكَ أُمَّتِي بِالسَّنَةِ فَأَعْطَانِيهَا وَسَأَلْتُهُ أَنْ لاَ يُهْلِكَ أُمَّتِي بِالْغَرَقِ فَأَعْطَانِيهَا وَسَأَلْتُهُ أَنْ لاَ يَجْعَلَ بَأْسَهُمْ بَيْنَهُمْ فَمَنَعَنِيهَا

I asked my Lord three things and He has granted me two but has withheld one. I begged my Lord that my Ummah should not be destroyed because of famine and He granted me this. And I begged my Lord that my Ummah should not be destroyed by drowning (by deluge) and He granted me this. And I begged my Lord that there should be no bloodshed among the people of my Ummah, but He did not grant it.

[Sahih Muslim 2890a]

 اسْتَأْذَنْتُ رَبِّي أَنْ أَسْتَغْفِرَ لأُمِّي فَلَمْ يَأْذَنْ لِي وَاسْتَأْذَنْتُهُ أَنْ أَزُورَ قَبْرَهَا فَأَذِنَ لِي

I sought permission to beg forgiveness for my mother, but He did not grant it to me. I sought permission from Him to visit her grave, and He granted it (permission) to me.

[Sahih Muslim 976a]