It's a protofascist phrase, part of the problems we have is people adopting this worldview, that life has to be hard in order to create "good men". It's used to defend rightwing social darwinism.
If anything, history goes the other way around. Fascism ("strong men") comes from good times, as a reaction. They create authoritarianism and discrimination ("bad times"), which slowly liberalizes and equalizes (gives rise to "weak men"). This makes situation better until another fascist takeover.
The phrase is commonly used amongst conservatives, yes. Labelling it “proto fascist” is ridiculous.
How exactly did you get to the conclusion that fascism needs "strong men"? The current US regime has nothing but the weakest, most fearful men clutching to power. You really think that Trump's call to execute senator Kelly comes from a position of strength? Your current bad times came from a few decades of weak men letting their fear and hatred (and greed) guide their vote -- strong men had very little to do with it.
Anyway, the quoted saying is not about any specific ideology, that's just your own projection. Here's the cycle reformulated without any specific ideology:
Hard times create strong men: hardship breeds discipline
Strong men create good times: discipline breeds prosperity
Good times create weak men: prosperity breeds complacency
weak men create hard times: complacency leads to hardship