I would think that undergoing a rebellion or civil war after which the form of governance changes marks the end of an empire, even if the territorial lines are not redrawn.
At the end of any given dynasty, it would be hard to say whether the empire is truly crumbling, or merely transitioning to a new dynasty. Who knows, maybe 1,000 years from now communism and the period of strife in the 20th century will just be seen as an unstable period preceding a dynastic transition.