Small Engines (Lawn Mowers, etc.): Engine stalling, starter solenoid, hydrostatic transmission

Question
I have a Craftsman 16 HP Koehler riding mower w/hydrostatic transmission. I stop to empty the baggers with the brake on, blade off, in neutral, and engine idling. When I try to release the brake the engine dies as if I had turned off the key. I can let it sit for 15 minutes ,re-start the engine, release the brake and continue mowing. It will stall again after mowing for 15 or 20 minutes. I've recently replaced the starter, solenoid, and seat safety switch. Thanks Mike Mitchell

Answer
 Hello Mike:

 If you have to let the Engine to Cool before Restarting it then the Ignition Module Is Heating Up.  Replace it and That will cure the Problem. If i have misunderstood please let me know.  Hope this Helps.

 Good Luck

 Respectfully

 John