Yup... our daughter's Suby-Doo did the same thing. We replaced batteries on it twice... and the first time the car alarm did that, I had to replace a pair of underwear as well...
It also was a car that seemed to have a lot of mystery battery issues. She would drive to work; and then it wouldn't start. I'd go over... wiggle the terminals... tighten them... then it starts... only to repeat the process at some random, maximally inconvenient time maybe a few months later. The alternator failed intermittently at one point... the battery went bad, we replaced it, then tested the new battery and charging system... the alternator showed charge voltage during a test, but then drained the new battery over time and essentially ruined it, by putting it through too many charge/discharge cycles. The part store gave us another battery under "warrantee" when we bought the new alternator. In the end, we never DID explicitly diagnose whether the battery killed the alternator or vice/versa... but replacing both solved the problem.
There were a lot of loads in that car. Nice winter vehicle... heated seats, front/rear windshield defrosters, a windshield wiper tray defroster... something I've never seen on another vehicle... but all of those winter features add to more points of failure, extra loads on the system, etc, etc...
Great car. Beast in the snow. Also a beast to troubleshoot.
Don't get me going about the ball joint mounts... on the bottom of the front wheel spindle... with about a full inch of a 10mm (maybe 12mm?) bolt threaded through a split knuckle. After a few years of road salt, the people around here that are into Suby-Doos just take the whole spindle off and take them to a shop to have the bolt drilled out, if they need to replace a ball joint. (the YouTube "how to" video on this is hilarious... some guy down south with a perfectly un-rusted car showing you that the process takes about five minutes... well... not here in NYS, the road salt capital of the world, lol)