Yes you are probably hitting the low voltage cut off in the hard wire kit.
And you want that CUZ ordinary car batteries ( lead / acid ) are not made for deep discharge, they are made to be 100 % charged all the time and then only having to start your car.
You can try and see in the morning when you start your car, if it have a voltage read out somewhere in the gauge cluster or on the dash, or measure on the battery itself if you have a voltage tester, but your battery will probably be down around 11.8 volts if not less.
With my original battery a few years ago ( 2012 car ) i had some problems testing a new dashcam, but the battery was not really displaying any signs of aging, but replacing the battery fixed that problem none the less.