This may be a problem with many auto reverse players: One direction works, but when you reverse, the other reel starts up but then something clicks and it shuts off. It is always the right reel that dies. The same thing happens during the FF or REW of this reel gear.
Excuse me if I don't have the nomenclature correct here. I've tried searching but found nothing. Did find the WM-10 tech tips. I am looking now at my own WM-FX55 (the one with the grey slider that covers the buttons).

First question--have you replaced the belt?

No. Could that could explain some of the erratic play in one direction and none in the other?

let me try to make a comparison but mabey i'm wrong. i have bought several players that were just fine for a while till they got some use and the belt stretched out. they were the simple auto-stop type. when the belt was stretched to it's new deminsion the auto-stop function also quit. i think it is a matter of resistance which the belt must trigger to make the function work. i have a couple of players with auto-reverse which were perfect at first but now they can only play fine in one direction. the other side worbbles very badly till it comes around again and then it is perfect. BELT GONE BAD !!!