Tough one !
I'd now check the set of contacts that are normally open, but will be closed when the score reel reaches "0", it may be "9". do this by switching the machine off, removing the score reel assembly and advancing the reel through each number. You will see the contacts close when the displayed number is "9" or "0" - I can't exactly remember. These contacts need to be clean - so do so with an old business card. Do this for all the reels.
How about this...
Record a few games - the score on the reels at the end of the game. then the score after the first attempt at resetting, and the second. I'm looking for a trend here.
Early on, Owen mentioned rebuilding the score reel assemblies... That looks to be a fix..But it is a fair job if you are new to them ! But there is no better way of learning how they work !