There is a pilot enable switch beside the blade controls, it feeds voltage from fuse f9 to the solenoid, and then heads to ground at the starter motor. I've seen solenoids that overheat, and become open, and once they cool down function again. But it's probably what you said, a loose connection. You'll need to determine if the solenoid is getting power and ground when the machine acts up, and go from there. You could also check its resistance while its acting up, and you might find that its become open.