The batteries in these cars are pretty weak: Pretty low CCA and not a lot of reserve capacity. It's fine for an original equipment battery but not something you'd want to keep if you've got accessories drawing current while off.
Also, a lot of people don't know this, but below 12V is a pretty deep discharge. 12V lead acid batteries are considered fully charged at 12.6 and fully discharged at 12.1V. If your terminal voltage fresh off of a drive is 12.55, that battery is pretty damn low, a battery with a healthy state of charge will usually loiter around the 13V range immediately after turning the car off as the surface charge dissipates and settle in the high 12's.
Also, many people don't know that a discharged battery takes hours upon hours to fully charge. Just the other day I took a battery that was at an even 12V and after 6 hours on a 12 amp charger it was still sucking in a lot of amps. Even if your battery was at a 100% state of charge, and you left your doohicky drain it to 12V, that is effectively a fully discharged battery, and no amount of driving will get it back to 100% charge, unless you drive constantly and burn through 2 tanks of gas without turning it off.
What you want to do is: 1) get a charger on that battery ASAP and 2) set the cutout higher, like 12.4 or even better, just get the battery pack
https://www.blackvue.com/product/b-112/