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.
Depends on how you look at it I guess. The history of the Chinese empire had periods of relative stability, separated by periods of rebellion, civil war, and strife, sometimes hundreds of years long. There were even periods where the empire was ruled by outsiders.
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.
By that metric, the United States ended in 1861 and another country took its place. The 13th-15th amendments fundamentally changed the understanding of the state / federal power dynamic.
