This is a YEARLY check on ALL mowers. More if you bag or side sling. Scalp the yeard, you better check it out. Over heating causes valve seats to come loose and so on. Look all around the cylinder/s cooling fins for grass, dirt, oil and junk.Although the above sounds like a fuel problem, it also sounds like an overheating problem. If you haven't removed all the housing to reveal the fins, please take a look. What I found under mine was a nice varmint nest. Just enough stuffing to let the engine run for about 5-10 minutes, then a shutdown, followed by a cooldown and start again. And yes, I did initially treat the problem as a fuel problem and totally cleaned the carb, checked the fuel pump, lines and gas cap. None of those fixed the problem; but cleaning out the fins (I used a power washer, but that was over-kill) had it running until I shut it off. Don't feel bad though, all those things you've already done, need to be done occasionally.
slomo