Without being there to look, it sounds like a fuel supply issue to me. The next time it happens, pull the top off of the air filter and look down the throat of the carburetor while you activate the throttle. Do you see a strong stream of gas coming out of the accelerator pump? If not you likely need a new fuel pump or need to rebuild the one you have. If you do have a strong stream, I would then pull the cover off of the float bowl and check for debris that could be periodically blocking the outlet. I'm sure others will have additional ideas.

Sounds like it could be vapor lock since it starts and runs ok from a cold start. 

@jason-hartmann

Hi Jason

I think Tiny has likely pointed you in the right direction, and the result of a weak fuel pump can lead to what Dennis has suggested.

I have had a weak fuel pump on an old John Deere combine that worked fine when cold, and even hot and fully load when at full rated speed.

But if I let the engine cool down and then shut it off, It wouldn't restart without someone blowing into the tank to pressurize it.

Once started, it worked fine again at higher revs.

Eventually it got weak enough that vapor lock became a problem with anything less than 1/2 tank of gas.

Installing our spare pump fixed it.

In my experience, vapor lock was an old Ford thing  🙂 and never happened on six cylinder Chevs unless something was really wrong...

like a weak fuel pump.