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?

Try resoldering the connector on the Solenoid Driver board and check the pin on the connector for that bank of targets.

I think Shockme is correct. You have to clean the leaf switch contacts. I use 2000 grit sandpaper for this and it works well. Place
between both contacts for each target when the targets are down and swipe a few times. Should clear it up.

You are correct with your logic. No answers here, but if you do clean contacts and they are the gold plated variety, use a fresh dollar bill or a business card that isn't glossy. Is the coil for the reset ok??

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.