Discharge is an issue, of course! I have a portable flashlight in the car. They recommend to store it plugged into the power socket in the boot but I have my doubts.
Going without the subwoofer can be worth a try. Increasing power consumption and decreasing battery capacity is a doubtful combination, incidentally.
The car doesn't turn itself off when you lock it. It stays on for a while before "falling asleep". The engine start/stop button remains lit I recall.
Do you really mean that you have the battery fully charged and the car tells you the battery is critically low? It should also disable "unimportant" consumers then: the electric heaters and even the cabin ventilator. I use the notorious "auto stop/start" function (in warm weather: it doesn't work when it's cold anyway) to check if my battery is fine and I don't need an extended (/higher revs) run to fill it up.