Why Or'd Vcc with backup battery output shorted battery life?

[jellis00]

..... but it is possible that the PIC is sinkink current through the 4.7K resistor even though the PIC is powered off.

I see what you are implying about a leakage path from the backup power source to the DS1337 through the 4.7K pullup resistors to the PIC. However, if the PIC is powered off that would mean the PIC pins that are connected to the bottom of the pullup resistors would have to be at ground level or at some voltage below the backup voltage. I don't have enough knowledge of the PICs to know whether that is the case or not. Do you or anyone on this forum know about this or where I could find out?

Can we see the whole schematic?

Here is the whold schematic: