You say the plane isn't a trainer. Is the engine cowled? It could be overheating in the air.

My first guess, though, is that you're running a bit lead. Try backing out the needle a bit more than you think you should.

Your symptoms are consistant with being lean and/or overheating.

If you fill the tank half way, does the problem happen on the ground? It's possible you have a hole or some other problem with the clunk line inside the tank which only shows up once the fuel level gets below half.

It could be fuel foaming as well, though I think this is less likely.