But I think there's a very substantial difference between empires past and the american one: Cheap, ubiquitous, high speed communications and ditto + safe travel.
Managing far-flung territories in the British and Spanish empires caused major, major friction, in a way that just isn't the case in the present day. Back then, colonial service was a life career, and you'd spend years at a time deployed overseas. Letters took weeks to turn around. Today, if you need the help of a specialist, you pick up the phone, or you could even easily fly one out and he'll be there tomorrow or the day after, and he'll be back home a few days later still.
A lot of American might is still inextricably linked with maritime power, purely because of those aircraft carriers and the support fleet that accompanies it.
In terms of the republic, I think that we're in a dangerous time. But we've been there before and came out ok.
I understand that the average case is pulled in either direction from multiple empires but I think it's useful to compare with empires with similar qualities and their longevity as opposed to comparing against the average case.
For example, comparing to Britain wouldn't make sense since the base of power was a much smaller landmass with a strong central governing tradition within the nation proper. Their empire was based on supreme naval and economic dominance, which was outmoded by the natural advance of technology.
EDIT: I've just noted the link below. I wouldn't say that the Ottoman Empire ceased to exist at that point but was perhaps less strong. Is the fall of an empire the decline in strength or the point in which it is no longer deemed an empire?