Sounds like a bad coil or ignition module
However the first thing is to determine if it is fuel or ignition.
Thus the instant it stops grab a can of carb spray & give a SHORT SHOT down the carb & crank the engine
If it fires then you need to look at the fuel system and in particular the fuel tank for accumulated debris.
In any case, remove the blower housing and check for a build up of debris , particularly around the heads which will prevent the head cooling properly and that can cause the valves to stick till the engine cools down completely.
If you have a low oil cut out fitted, bypass it ( pull thge plug off & tape it over to prevent grounding , these do occasionally go bad with heat on the small Honda engines & they all work the same way