Anyone had this happen?

[Dean Romig]

You may have a bit more of a problem than what is immediately obvious.
If the screw backs out and the plate starts to pop out of place you need to check the edges of the tapered slot cut into the doll's head that accomodates the stop plate. The stop plate is hardened but the edges of the slot on the doll's head, not so much. Those edges are critical to the fit of the stop plate and can bend over, or out.

I just saw Brad's comment and his remedy is probably the best permanent remedy possible.

Brad, the stop screw you recommend will take considerable pounding from the ejector rods over time so it needs to be hardened to resist being damaged. The section of the screw that accepts the pounding would necessarily need to be cut below the threads to avoid damage to the thread - 'free shank' in other words... right?