One likely source of the problem is a failed Ready Start thermostat. This is mounted behind the muffler with the same 2 bolts. Its visible under the blower cover. it opens the carb choke via an air vane when the engine is hot. To check if this is your problem, warm up the mower and then remove the air filter. Look at the choke butterfly at the carb opening - if its closed all the way, the problem is likely with the thermostat operation. Check this video for some better illustrated repair info:
http://www.youtube.com/watch?v=Z3XP5mz59mA

Well, I checked the thermostat and the carb choke and they both work as they should. So that eliminates them as the culprit.

I also changed the oil, not because I believe that may be the reason for my issue. It still had the factory oil in it and I figured it was due.

Any other ideas or suggestions or ideas?

You might have a heat sensitive coil that will produce enough spark while running, but not enough to restart.

Check the quality of the spark with a cold engine and then compare that to the spark quality when you have the problem.

Clean your cooling fins. This may make that "slight" amount of difference, temperature wise.