Quoted from Palooka61:the way I read it, it indicates that at the end of the reset cycle the A relay is unlatched.
I think you've got your terms tangled up. The manual doesn't use the terms "latched" or "unlatched" that I can see. Ordinarily the A relay is latched, or waiting around to start doing its thing. At the start of reset the A relay coil fires which trips or unlatches the relay which means that the A relay is doing something (like running the Score Motor). Once the reset sequence has completed the A relay is itself reset or relatched with its own A relay reset coil.
Think of the A relay as a trip relay alone in its own trip relay bank. The A relay coil trips the relay just like a trip relay coil would. The A relay reset coil resets the relay like the reset coil of a trip relay bank would. The only real distinction between trip relays (or drop targets) and interlock relays is that trip relays have to share a common reset coil while interlock relays have their own dedicated reset coils.
Your A relay is not resetting reliably which is a common problem with many causes. I would start with the easiest remedies and work your way toward the more complicated ones. You know that the A relay reset coil is getting a pulse but there's a small chance that the pulse is too short or too weak. Checking, cleaning and maybe adjusting the Score Motor switch that sends the pulse would be an easy place to start. After that try cleaning the two armatures where they rub against each other. Next maybe try removing the one armature that comes off easily and try cleaning or polishing one or both armatures. Swapping in a new armature might help if the two armatures have developed a wear spot between them. And so on. There are lots of topics about intermittent interlock relays here. Search for "AX relay"...