I think you are looking in the wrong direction-solution for your problem. This tractor has the infamous "Time Delay Module" and they are known to cause a pain you know where. It's bolted to the left side of the engine right next or near the starter. Probably a round black devil with several wires going somewhere, where there is trouble brewing.
Here is one remedy to see if it is the problem. When the engine quits again, take a wooden or plastic handle screwdriver and "slightly" tap this dude. Not to hard, just enough to wake it up. If the tractor starts after you have done this, you now know what is the problem. You can buy this piece of plastic...TDM on ebay for about $20.00