So now it's a mission to get this one figured out! I would try a spark plug (verify that it's the correct plug) and if that doesn't fix it, a carburetor clean, or even even think about replacing the carb (mine are less than $15) Not worth the time and parts spent cleaning.
Does your carb have a drain on the bottom of the float bowl? The next time it quits you might crack that and see if there is A: fuel and B: water in the fuel. It doesn't take much. I have had my mower quit after a bit only to find water contaminated gas. I attributed that to the ethanol enriched gas I was using. A local gas station now has Recreational (ethanol free) fuel. I haven't had that problem since switching over.