Two things come to mind. the ignition module is heat sinking and loosing spark, the fuel solenoid is heat sinking and shutting down fuel flow. Some of the courage engines used on Troybilt had issue with the heat from the exhaust would damage the fuel solenoid on the carb.
There might be fuel in the tank but that does not mean there is fuel in the carb, or more over, enough fuel in the carb.
Easy one first, undo the fuel cap about 1/2 to 1 full turn.
If you hear a sucking sound or the mower runs fine then the fuel tank vent is not working.
No joy there give it a quick squirt of starer fluid ( just a little ) or a few drops of fuel strait into the carb.
I it starts & runs a few seconds then you have an obstruction between the fuel cap and the main jet in the carb
No joy here either, get an in line spark tester and see if it is sparking when hot,
Very common for an ignition unit to go bad when it gets hot.
