Well, you're making my point: for millenia people have been saying that 'the end is near' but it never seems to materialize. (we can wait for 12/21/12 and see what happens).
The 'empires/cultures' you name have changed in context, but the Chinese, Italians (Romans), Greek and Russian PEOPLE are still with us, living, working (well, not the Greeks <grin>) and interacting in the world.
My personal view is that the USA (culturally) died several decades ago but through it's own inertia just hasn't fallen down yet...but we venture on today with our individual lives.
Therein is the 'self correcting' piece. It's never as bad/apocalyptic as 'they' say and somehow, even though things/names change, they keep running through tweeks and 'cultural shepard moons' rather than end of the world scenarios.
Again, (just an example) by now we were supposed to be riding bicycles and reading by candlelight because 'all the oil would be gone'....and suddenly we start finding new oil fields and new methodologies to access huge, previously untappable stockpiles.