Dave. Each drop target has a leaf switch behind it that closes when the drop target falls, telling the game it was hit. If the switch is flaky or not making good contact, ie dirty or out of adjustment, the game won't know it's down and therefore won't reset until the next ball. Check all the switches in that target bank to make sure they are doing their job. That would be the first thing I would try.
I see you have a ton of games and lots of years here, so you've likely checked this obvious stuff already eh?

The transistor for the reset coil might be bad. You should have a look at that, as well as the connector and pins on the solenoid driver board as Sealclubber suggested.