I was reading alot about the Fatimids, especially their administration, and I really think that there was nothing preventing them from fielding the sort of military power that the later Ayyubids and Mamaluks possessed. Their main problem was their need for powerful leadership from the top: the Caliph and the Vezier had to be strong.
Badr-al-Jamali and his son Al-Afdal Shahshinshah were effective commanders and leaders for a Fatimid state in need of a more centralized military and bureaucracy. Can a TL be possible in which their "style" of regime continues and the Fatimid dynasty survives?