I can name you two empires that has stood the test of time and are still around, India and China.

As for the cause of the fall of The Roman Empire, which is what we are discussing here under the guise of chronology, I can but say that the more I learn, the more I learn I do not know. My specialisation as a historian is Danish Viking- High Middle Ages, secondarily Iron Age and Roman history (I would estimate that I have read 20k+ academic pages on Roman history), so I know a lot, but not enough to say what caused the fall of the empire. And I think that no one can ascertain it for certain, nor that it was one single cause. Nothing in history is caused by a single cause. probably internal dissention, economic weakness, demilitarisation/military weakness and some ideological changes as well that all played their role in the fall.

Were I to wager a guess about when the empire was doomed I would say 406 AD when Stilicho pulled the border garrisons away from the Rhine, allowing the Vandals, Alanss, Suebi and Burgundi to overrun the Western Empire where the Goths were already on a rampage (on New Year's Eve no less). The Empire never recovered from that, even though most of the Germanic Kings and Chieftains would gladly have settled for a high place in the Roman System and a place for their tribe to live. The Empire was deteriorating and they instead had to build new realms on its ruins, Bachrach has some insightful points about the integration of Roman and German, mostly in Gaul -> France.