Just a thought. if you have another key fob try using that one.
maybe with the one you are using the button contacts could be defective. like being stuck down. causing the locks to constantly try to lock. Not only will it cause your car battery to drain it will also drain the Fob battery.
On some factory alarms if you press it once it will lock the car and set the alarm. if you press it again the car horn will beep. it is not necessary to hit it a second time, but some people need to hear the horn beep, so they know it is set.
I would definitely replace the battery in the fob, and at the same time check to see if it’s reasonably clean inside, blow out any dust and grime, and definitely do not leave it in a heap of stuff in a purse or pocket overnight.
If I had that problem, as a first step I’d ask a shop to check the battery and charging system. If your battery was iffy during the summer, now w/cold weather it could be downright bad. If both check out ok, I’d ask them next to verify the driver’s door switch is working correctly. Could easily be caused by something else, but those two are pretty easy shop checks.