Also, the battery's only purpose on most mpu boards is to keep power to the cmos ram when the machine is powered off so that the bookkeeping data and other info stored in there doesn't get scrambled. We've had cmos ram chips go bad in a way that they drew way more power from the battery than normal, thus draining the battery much faster than normal. If your cmos ram is socketed you could try replacing it, usually just a chip change.
Another thing to watch for would be stuff on the board around where the battery is connected that would provide a path for it to discharge, like if there was a residue from a spilled drink or previous battery leakage. But since you've been replacing the batteries already you probably would have noticed something like that.