Originally Posted by RebelR

Sounds like a fuel issue to me. Either there's some varnish somewhere in the carb that you aren't seeing or you could have issues with the lines themselves. May be time for a carb rebuild. Check for rot and pin-holes in the lines. I've had small engines do the same thing in the past and it always turns out to be fuel related.

On the off chance it's not. Check to see of there's any slack in the safety cable that shuts off the ignition (I think most mowers now have this). If that cable stretches it can sit right in the cusp of being engaged. I had a mower that would run and when it heated up it was just enough to shut it off. Adjusted the cable and it worked fine after that