2011 Subaru Impreza - is it possible to leave the engine running and lock the doors / enable the alarm?

I live where it’s gotten down below 0F and don’t drive my car every day. Twice this week the battery (which is only about 14mo old) was mostly dead, and I had to plug in a charger.

I have two keys but only one fob. If I start the engine I cannot lock it with the fob, and if I try to lock it before closing the door it unlocks immediately. If I manually lock it it does work but I don’t know if the alarm is enabled.