I think the case of Rome is exactly one of the ones where people get history extremely mixed up. The Roman empire was powerful and prosperous for hundreds of years - more than any other empire in Europe in history. The vast majority of people of those prosperous times created more prosperous times, again and again for those hundreds of years. Rome only fell because of an extraordinary amount of bad things happening at the same time, not because "easy times create weak men, and weak men create hard times".

Basically, by the model of the quote, we shouldn't expect any prosperous society to exist for anything more than 1-2 generations.

Even looking at the times after the fall of Rome, it took many more hundreds of years to get back to the prosperity of the earlier times - so the "hard times create strong men, strong men create easy times" part of the quote is also false.

Edit: As a complete aside, there is a particularly hilarious take on the history of Rome that made some splashes in right-wing circles, by a ridiculous self-proclaimed intellectual named Stephen Molyneux. Among many other historical inaccuracies, he was taking quotes from Cicero about the moral decay of Roman society to show how that "moral decay" led to the fall of the Roman empire - of course, Cicero didn't even live to actually see the Roman empire or its peak, nevermind its fall some 500 years later. If anything, Cicero's "moral decay" could be said to have led to the rise of the Roman empire.