Could be a clogged air vent on the gas tank. Next time it happens pop the tank open and listen for the sound of air rushing in. Then try to start it right away.
It doesn't take 2 minutes to fill a float bowl (unless your fuel filter is clogged - so check it). You could be overheating the engine, or you may have a slight flaw in the ignition that expands when hot and turns into a bigger problem... Check the fuel tank venting, then the fuel filter...
FWIW: If it happens more on a full tank then it's the tank vent.