With such limited use you should have your own battery charger and recharge the battery every 2 to 3 months.
There are a number of computers in the car that draw a small amount of power to maintain memory, perform self tests and remain on stand-by, you want the doors to unlock when you push the button on the remote for example.
A battery shouldn’t go dead in 2 to 3 weeks but with your driving schedule the battery will be in a very low state of charge and won’t last 2 weeks.