Small Engines (Lawn Mowers, etc.): Craftsman mower stops running, m274 mule, safety relay

Question
Paul,
No tank questions from me, but I did recently acquire an M274 Mule that I will be rebuilding in the near future...

My real reason for contacting you is to ask your advice on my Craftsman riding lawnmower model no. 917.276021.  It stops abruptly after about 20 minutes of riding.  I have checked the fuel system and use a fuel stabilizer.  I removed the starter and cleaned the contacts on the starter.  It then started right up.  Then after about 20 minutes it stopped again.  When I try to restart it, the starter does not spin or engage.  After complete cool down it will start again.  The engine is a Kohler model no. cv730-0017.  Any ideas?  Ignition module?  Thanks for your time and expertise!

Answer
The fuel system and the ignition module have absolutly nothing to do with the starter spinning.  The only component involved in the cranking system that can be heat related is the solenoid and the safety relay.

Neither of these items will cause the engine to die.  

Let's solve the cranking problem first, probably the relay #109748x. Then we will deal with the engine dying