I bought my first A-1 in 1983 and used it extensively for about a year, at which time I discovered Canon's classic mechanical cameras of the 70s (FTb and old F-1). But I continued to use it as a back up system for several more years. Since then, I've owned a lot of A-1s and I currently own an almost mint example that doesn't get as much use as it should.
There was only one occasion where my A-1 had a drain issue and that was when I was out in the cold with it. It lasted for about a half hour before the battery quit, but that's something that will happen to most any electronic camera, Cold weather drains batteries, no getting around it. That's why some camera makers have offered remote battery packs, so they could be kept someplace warm, allowing the camera to continue its normal operation. Other than that one occasion, I don't recall that A-1 going through batteries faster than they did on my AE-1.
The A-1's battery check feature has a blinking red LED. The fresher the battery, the faster that LED will blink. It's almost a blur with a fresh battery, and with one that's on its last legs, it will blink very slowly. Now, it seems to me that Bob can monitor battery consumption using this test feature. Bob, you might be able to pinpoint at what point the drain becomes apparent, or if it perhaps is just draining the battery quickly. This should help you in deciding how to proceed.