If you stretch the quote for a long enough time, it becomes trivially true and completely not interesting: any society that falls was by definition in "good times"; and every society that rises was, by definition, in "hard times".

The quote implies though that there is a deterministic process: good times can't help but create weak men, and weak men can't help but create hard times. This implies a rather limited time frame - if generation after generation of people living in good times keep creating good times, then it's hard to take the concept seriously. Similarly, if generation after generation living in hard times keep creating more hard times, the other part of the concept fails as well.

Even worse, while it seems to be true that every successful society eventually falls, it is demonstrably false that every failed society eventually rises. There are numerous peoples who have been utterly destroyed without ever rising up; and there are regions of the world that have never been prosperous, or at least not for hundreds of years now.