the coil yanks the armature plate a lot harder/faster than you can, so if pieces are worn you may have your problem.
the one thing you can do something about is the position of the brass finger that prevents the shaft from turning backwards when the pawl is pulled back (pawl = the plastic pusher you are having trouble with).
make sure the finger has good tension against the ratchet and is positioned to hold the ratchet so it can't spin the wrong way. Loosen the screws to slide the finger to position desired.
look for other adjustments to the armature plate position ... the goal is the pawl retracts enough to reliably grab the next ratchet tooth, but not further.
if your problem happens often enough, mark one of the big alternator teeth with a sharpie and watch as you hit whatever playfield thing makes the unit step. You want to see if the shaft turns backwards or the pawl is slipping off the edge of a worn ratchet tooth.
part numbers are for a 10 step unit are:
3A-7366 - pawl
A-7595 - shaft with alternator
12 step unit:
3A-7369 - pawl
A-7567 - shaft with alternator
I don't remember if the coil screw has a brass washer on it, but if it does make sure it's between the coil and the frame (not under the head of the screw). If it needs a washer and it's not where it should be, that'll make the armature plate pull the pawl back further.
what game is it on?