That has only one Bank Reset Coil, right? Had you already cleaned and adjusted the
Bank Relay contact that runs off the score motor's cam? Also, I found out it to
be a good idea to clean the bank reset bar and the relay plates where they both contact
each other. I clean by putting a solvent (I use carb choke cleaner) on a small piece
of scotch brite and cleaning both the bar and the relay plates, then after wiping
off cleanly, I apply a lite grease so there's no friction (or grabbing) when the bar
makes contact with the relay plates. Also, I clean the coil's plunger with Lemon
Pledge which safely takes any stickiness away.. (T)

Perhaps taking the plunger out of the coil and cleaning it along with
its sleeve will help. The bar has a return spring right? Possibly it's been
replaced with too strong of a spring. I'm sure you checked the pivot
joints for excess sloppiness..
And you said that you cleaned the bar and relay plates and applied
a thin film of light weight grease to the bar..

Watch the reset bank while someone else pushes the start button.Test the hold coil on that relay to make sure it's getting electricity (it should NOT be 115v at that coil!). If the coil passes the check, move on...

If you have some that aren't locking, look at the lock spring for that relay.

If you can push the locking relay in manually and you know it works, it's probably a mechanical issue not an electrical one.

No, actually the Bank Relay Coil needs to reset the Bank Relays before the pins are in
the totally reset position. The score motor fires the Pin Reset Relay before the Relay Bank
Coil, but the Bank Relays reset before the pins get to its total reset position. If the pins
totally reset before the Bank Relays did, then the Bank Relays would tell the pins to go up
again.
So if I remember correctly, the Bank Relay Coil energizes, but doesn't seem strong enough to
reset all the relays, right? Not sure why it wouldn't, but did you check to make sure 115V are
getting to the Coil? If so, and you lubed all of the banks pivot joints, maybe a weak coil..
The reset bar has a return spring, correct? If the spring is taken off, does the coil reset the
bank relays then?

Oh, on your machine the pins trip the relays. Yes, I forgot. On the earlier Uniteds, the relay tripped
the pins. So with the machine reset, and you trip one of the pins manually, that corresponding relay
in the bank will energize. Sorry, I knew of that set up, but forgot. For United, I've restore mostly
the 50s Ball Bowlers..
So now your figuring was right. As soon as a pin energizes its bank relay, a set of contacts in that bank relay
opens which cuts the circuit to the relay so that it doesn't remain energized. So now, the pins do need to
reset before the Bank Relay resets so that the pins contacts open before the Bank Relays closes.
It must be that the Pin Reset motor is running slow. I believe that it's a 42 RPM motor. It may need to
be taken apart, cleaned and regreased. But before you do that, you can try this. On the pin reset motor,
the armature pulls in when energized, and back out when not energized. There's a small tail on the back of
the armature that when looking carefully you can see pulling in when you manually push in the pin reset
relay. When not energized, you can put a couple drops of light weight oil on that tail, then energize the motor.
This may help give the motor its proper RPMs and help with the problem. I'd give that a quick shot first..

Your Bowler requires for the pins to totally reset before
the Relay Bank Resets. Is the pin reset motor 42 RPM?
It should state on the pin reset motor label, (and schematic).
If so, you can detach the push rod from the reset cam
and run it for 30 seconds by holding in the pin reset relay
and count the RPMs to see if its around 21 (or 42 for 60
seconds). Maybe you can try that next..