Well, how about acting like the American colonial leaders in 1776? There once again we find a group of prominent local citizens of a far-flung, slow-communication empire deciding that their own interests would be better served by grabbing control for themselves.
Any time a region has a tenuous link to the center of power, you're going to see this pressure to split off as an independent entity. It doesn't even have to be violent. E.g., Roman Britain just sort of faded into being plain old Britain as the power and reach of the (very) distant imperial core faded out. Nobody woke up one day and said "Hey, we're not Romans anymore!" But in 300 CE they were very much Romans, while in 600 CE they very much were not.