The score reset relays are pulsed via switches on the score motor. The schematic on ipdb.org is too low resolution to read the score motor section very well, but assuming you have a schematic look for the switches on the motor responsible for pulsing the reset relays. Ensure they are clean and making good contact as the motor runs.

Check both — although if neither relay is energizing then the start relay switch seems more likely since it is in common with both reset relays. Manually close the start relay when the power is off, you should see the switch in question close and flex slightly. If not adjust the gap.