Check the fuse holders on the flipper boards. Press down against the middle of the fuse. If the fuse holder clip splits then it might have been a cracked fuse clip that was only working part of the time. Something quick and easy to try.

If there is a short, blown TIP or pre driver it would energize the coil and pull the plunger into the coil. The flipper would be stuck in the up position. When the power was turned off the plunger would go back to it's normal position. Never heard of this "backwards" problem of it being held in the down position unless it was something mechanical. At this point if I was you I would switch the coil to the other flipper and see if the problem follows the coil. If it does get a new coil if it doesn't I would take a close look at the flipper assembly. To see if there is something put on wrong.
Very strange problem. Good luck with it.