I really don’t see the US disappearing any time soon. The Roman and British empires fell apart, leaving merely Rome and Britain in their place. However, the US is not an empire (despite the cries of some of its naysayers), so it can’t lose power through loss of its territories. The US could certainly lose its status as World’s Sole Hyperpower, though even that won’t happen in the foreseeable future.
The US derives its power from three main sources: military, economy, and democracy. The first ensures that nobody is going to invade us. The second ensures that we’re not going to go broke. And the last ensures that the people here are happy enough to not rock the boat too much. Sure, there’s constant change going on, but nothing on the order of revolution, and no serious group that could plausibly institute such revolution. We’re pretty strong, and we’re pretty stable.
So what could affect that? Democracy? It’s not going anywhere, and nobody’s pushing to get rid of it. The people here rightly recognize that democracy is the best way to get things done, so as to preserve everybody’s rights, while keeping the majority happy. The economy? The freedom we enjoy here keeps our economy pretty much self-sustaining. We have our ups and downs, but at our worst we’re still ahead of most other places in the world, and an order of magnitude better than the third-world folks.
That leaves the military, the only front where there’s anything approaching a significant effort to hobble our capabilities. Of our three strengths, this is the one I could foresee falling apart, at least a bit. Given a long enough period of prosperity, the anti-military people could coerce the government into severly downsizing our forces, until our ability to project (and protect) ourselves drops down to European levels. However, if that were to happen, eventually someone would hit us, and that would be all it took for our military to ramp back up to existing levels.
I think the only things that could seriously destroy the country are either the sort of things that are impossible to predict (say, an asteroid wiping out the eastern seaboard), or are so far off in the future that it becomes impossible to make any educated opinions. In 10,000 years, who can say? But I feel it’s a safe bet that the US will still be here in several hundred years.
Jeff