I would agree on the ignition module. Almost a guarantee it. When an ignition coil starts to fail after it heats up it will die and won't restart until it cools down. If you can if it dies on you again take the plug out and connect the lead wire to the plug put it against the metal block and have someone turn the key. Obviously taken care not to be in the way of the machine. look between the diode and see if you have spark. If not this should be your issue. If you want, you can look up the model and serial number off the engine and give them to me and I will look up the coil cost or you can do it your self at http://www.arcolawn.com/pages/OemParts
Hope this helps
Hope this helps