Engine simply stops

Welcome!

It sounds like it could be losing spark. I would get a sparkplug tester on there and see what happens after it dies and doesn't want to start again.

Take the gas cap off and run it up and down your driveway. It has the classic sound of a plugged vent on the cap.

possible coil breaking down...my jd did that would run maybe 5 minutes then shut off, after it cooled down would run another 5 mins then shut down...checked everything and ended up being the coil...changed that out and all is good , check to see if you have spark right after it shuts down

Welcome to the group Callicles. As you can see, it could be different things, but I agree with Michael, it sounds like the gas cap vent could be plugged. Try taking the cap off, or just loosening it and try running it for a bit to see if that does the trick. If so, a shot of carb cleaner to the vent hole, or a new cap might be all you need. You might also try blowing some air back through the fuel line to clear anything that could be floating around in the fuel tank that's blocking the hole to the fuel line. If eliminating clogs in the fuel line doesn't do it, then go to the next step of checking for spark.

Ethanol?

Thanks, everybody! I tried different things, including the gas cap advice and the carb cleaner. My best guess now is that ethanol was/is to blame. I'd been adding fuel stabilizer, but by doubling the recommended amount, I was able to get the thing to stay running. Strange!

Good deal! Sounds like you may have just run across some bad gas, or it got stale.