Although Saladin is well remembered for fighting the crusaders, sadly, the rather large empire he created didn't last long after he was gone. So how could it have survived longer and what would have happened if it did?
The Mamluks managed to hold together a pretty impressive Empire for a long time. What did they know that the Ayyubids didn't?
Question to the OP: If the Ayyubid Empire develops a mechanism of succession that allows for the current top dog to be proclaimed sultan, would it still count as 'Saladin's Empire' once that has happened a couple of times? Because that is the easiest pathway I can see, where the Ayyuibid Empire basically provides administrative continuity for a transition to Mamluk-style rule.
Well, in a sense. He did found it. I suppose someone might refer to the USA as Washington's republic.
But really having a clear succession is what could save it.