My car has been in the garage in Maine all winter. I start it up about every 2-3 weeks. No battery maintainer, and as far as I know it's the original battery.
When I do start the car, I make sure to drive it around town until it reaches normal running temperature. This also gives the battery time to regain the charge it lost to starting the engine. If you just start the car and let it idle for a few minutes, I doubt the battery is getting recharged.
I would suspect a parasitic load on your battery somewhere.
YMMV
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