The outhole relay will be activated by the outhole switch making. It will pull in and lock on via a switch on that relay and the score motor runs. There is a normally open score motor switch that will activate the outhole coil and kick the ball up, another normally closed motor switch opens and releases the outhole relay. I own the game but I can't get to my schematic right now. What you want to do is find on the schematic the outhole relay and the outhole coil, and locate, clean and adjust all switches in those two paths.
If everything else is resetting, I don't believe the game thinks it is in game over. Something is causing the outhole relay not to activate. Are you sure the outhole relay coil is good, no broken wires etc?
Try this test. Start a game, and then manually close your trough switch. See if that steps the ball count unit to ball one and gets the playfield live.