Agree, would expect a higher charge rate. Was the registration done correctly, its what sets the initial charge rate? If you have Carly you can check & re-register it yourself.
Also if the system is shutting something down you need to find out what it is. Most likely the source of the drain if there is one. It might be shutting something down that is normally active because the battery is not being sufficiently charged.
We have devices on the BMW that go to sleep with the lock but many are still drawing amps to keep their memory settings alive.
FWIW my Cobra has been inactive for 3 months due to a house renovation dumpster blocking it in the garage.
Car fired up on the first key turn without any outside battery support like a trickle charge etc. It has a ECU & entertainment system that stays hot, to preserve their memories, when the car is shut off. Its a low amp draw but still a draw.