In addition to what Hail Ants said about the Roman Empire, don’t forget the mass migrations of various barbarian groups into the Northern territories of the Roman Empire. And that while the western half of the empire fell in the 5th century AD, the Eastern half kept going for nearly a thousand years more. Of course, the last time I checked, the US hasn’t really had a problem with roaming barbarians, unless you count a bunch of migrant Mexicans looking to pick our lettuce & flip our burgers. 
One large factor in the British Empire’s decline is that the UK’s power base consitited of an island core, and several far flung territories. While most Canadians, Australians, New Zealandlanders, and some South Africans would have been very close culturally to their relatives back in the UK, the rest of the Empire’s subjects (Indians, and all the mass of cultural groups on the subcontinet, a myriad of different African tribes, and so one) didn’t really consider themselves British, and were constantly wanting self-rule & independance. And even the more culturally British wanted to control their own affairs.
After the British wore themselves out fighting other great powers in the two world wars, they were not able to contain these independance movements, especially since some were being funded & backed by another great power (the Soviets) and in the largest British colony, India, Gandhi managed to get a resistance technique (non-violent resistance) going that couldn’t be defeated by conventional arms, without the British public back at home getting queasy.
Of course, the US really doesn’t have this problem - the vast bulk of US territory is in a continous land mass, with most of the population considering themselves as Americans, with most of the rest being one large, sparesly populated hunk, of which most of the population considers themselves American. While the USA has occasionally grabbed bits of far-flung territory, held by people who don’t really want to be Americans, we have either filled up those territories with Americans - think Hawaii, kept them for a little a while, then gave them independence, after we get a reasonably friendly, reasonably democratic government going - think the Philliphines, or what will probably with Iraq, or acted as a reasonably benovelent protectorate, of small islands that would have a difficult time operating as independent countries - think Guam or Puerto Rico.
I think a look at the rise and fall (and rise again, ect cet) of another large, continetal nation, with a reasonably homogeous population like China would be a better example of how to predict when/if the US will “jump the shark.”