Sounds like a problem with the carb. When it heats up, it expands and the passages change shape, causing the mixture to lean out and stall the engine. If its less than a year old, you should still be under warranty.

A broken gas cap was causing gas vapor lock that inhibited the gas flow to the carb. This is a two piece gas cap (cap and seal). Since the seal had broken away from the cap, the seal was thrown away and the cap attached tightly to the poystyrene tank. Apparently, without the seal, the tank was not able to breathe properly. Well this is kind of what was explained to me. Hmmm ... I Guess. Anyway, a $4 gas cap fixed the problem so far.

I had the same darn thing happen on mine and small engine places wanted to charge like $70.00 an hour to look at it.Well on mine it has a primer valve press 3 times before starting well the rubber boot for some reason would suck in and then it would do exactly what you are saying.I cut a little slit in my rubber boot seemed to work I haven't had a problem now for over 3 weeks.
This is just what mine did if your rubber boot isn't sucking in after awhile then it probably a different problem but run yours again like normal and see if it is getting sucked in if it is,put a tiny cut in it.

There is a suction tube on the carburetor inside the gas tank.This tube has a screen or filter on the end for keeping trash out of the carburetor.The screen can become clogged or coroded and create your problem.I would not reccomend cutting a primer bulb.Even if this did make it run it means you have a plugged port inside the carburetor.This screen can only be reached by removing the carburetor from the gas tank.Good luck!