If D2 is leaky or shorted, then the batteries would try charging from the 5 volt line, These don't like this and will probably heat up, leak or explode and defiantly not last very long. If D2 is open, then your batteries will not be in the circuit at all, but will keep charged, you will loose all of your settings.
D1 prevents the batteries from running the entire CPU, allowing only the Ram chip to draw current. If D1 was shorted then the batteries would run the entire CPU , resulting in extremely short battery life. If D1 was open, the batteries would run the ram chip when the game was shut off as well as when the was running. I would think this would
affect the battery life, but not to the extremes you are mentioning
Of course you could have a bad ram chip.
That is about everything that has to do with the Batteries
Of course I am assuming the layout of this board is the same as the Bally origanal