I took a pot-shot at the idea of cyclical approaches to history in this follow-up comment recently. My own view, as expressed there, is that these sorts of models tend to be more descriptive than explanatory: that is, they tend to align well with how things happen, but tend not to have a particularly strong ability to explain why. Obviously 'how' and 'why' can overlap a bit, so what I mean by that is that the way in which, say, an empire falls tend to be pretty clearly articulated, but the question of what factors lead to said process kicking off, or influence the rate at which such processes may take place, rarely are to any useful degree. So a cyclical model might explain, for instance, how the Ming fell after about 280 years, but it wouldn't really explain why it lasted 280 years whereas for instance the Sui lasted only around 40 before being usurped. They also fray a bit at the edges if not unravel entirely: they tend to have a pretty firm description of how iterations of the cycle end, but the resultant situation, and the circumstances and process by which a new iteration is supposed to begin, tend to be quite chaotic and defy attempts at codification.

There's definitely room for a more in-depth discussion on this, however, and one which I would welcome.