Inherent in your question it seems to me is the thesis that all Empires fall for pretty much the same reasons. I don't think that's right at all. Empires by their very nature are exceptional things, and thus inherently unstable in the long run.
I think the Anna Karenina principle applies to societies as well as families: Successful societies are all alike; every failed society fails in its own way. In other words, a whole lot of things have to go right, and keep going right, for a very successful society to stay that way.
So you could maybe come up with a grand unified theory for how they come into existence, but not for how they fall.
As fate would have it, while I'm typing this answer, Jared Diamond is on NPR delivering his critique of a new book on exactly this topic. The book is Why Nations Fail, by Daron Acemoglu and James Robinson. Diamond was fairly critical, but still you might consider checking it out. Otherwise, you could consider reading his own book on the subject: Collapse: How Societies Choose to Fail or Succeed.