First of all, how long will the United States last as a nation? Indefinately. The world is far more stable today. Once upon a time, states came and went with alarming regularity and rapidity. However, today, this does not happen much at all. It is far more common for states to break up with separatist elements gaining independent status while leaving a rump state that is generally recognized as a continuation of the original state. For example: Soviet Union - Russia; Yugoslavia - Serbia; as well as Eritrea breaking away from Ethiopia, Kosovo breaking away from Serbia, among others. It did not signify the demise of a state, but rather the creation of a new state leaving a rump state to continue the international rights and obligations.
How does this affect the United States? Well, even if the United States does decline and is no longer the world's leading power, it doens't mean the United States will die. It has a tremendous resource base and an innovative population. Will the United States break up into small pieces? Yes, there was a civil war a century and a half ago and there is the so-called blue-red "divide" but will this actually result in the split of the United States? I don't see it.
So, the answer to this question is the U.S. will remain indefinately. The international state system is more stable today than at any point in history. It would take a major cataclysm to change that anytime in the foreseable future.