The fuel I don't believe is an issue, unless the fuel is bad, any fuel should work in any brand engine the same
From your discription, it sounds like it's getting hot and loosing compression
What does the compression feel like when it's cold compared to when it's warm

My guess is you have zero compression as it gets warm, that's why it starts back up again after it cools down.

if the compression is bad a new piston and sleeve for those are cheap, for that matter a whole new engine is cheap.

Good luck