Battery Discharging overnight but small current draw?

So I have a few issues going on with my 93 325i. I bought the car about 2 weeks ago and installed a brand new group 48 battery from walmart. All was fine until I let the car sit for 2 days. I think the passenger door didnt latch fully and the battery discharged down to 10.5 volts. I jump started the car and drove it for about an hour. I know this really isnt enough time to charge the battery. Since then it seems every night the battery discharges low enough that I cant start the car. Ill check the battery when I park and it will show 12.6 volts then in the morning only have 11.3 or so. I thought maybe I had a parasitic drain but when I hook up my multimeter in series on the negitive side, I only see .01 amp draw with the key off. I did have the notorious trunk wire harness issue and I took care of that yesterday with some electrical tape.



So really I have 2 questions, does leaving one door open slightly keep the computer awake and

would the battery be discharging because it discharged so low and has not been fully charged back up yet? It has been bitterly cold here recently (in the single digits overnight).



I finally got a hold of a battery charger today, and I am going to charge the battery overnight.

Battery Discharging overnight but small current draw?