What inspires you to persevere through adversity?

Perseverance is overrated.

If I have to persevere, then I do. It doesn't require inspiration. It's just doing whatever thing is mandatory.

If it's not mandatory, then I take my best guess about the long-term outcome. And if the risks seem to outweigh the rewards, I quit, and do whatever seems better.

I've got a lot of reasons for that, but the primary one is me sticking with my startup for waaaaaay longer than anybody would say is reasonable. Winners never quit, and quitters never win, but those who don't win and don't quit are idiots.

Going through a difficult time.

In my personal experience, a divorce, money (child support), if I couldn't change it, I'd ignore it. But to ignore my own adversity, I had to intensely focus on something else, typically a new interest or hobby. I dove into medieval history, and now have a suberb library on on the topic - the reading and the collecting books both informed me and kept my mind off the troubles I couldn't avoid. And I dove into baseball which to be honest, broke my heart but baseball despair is an infinitly more palatable despair than love loss.