Unless the battery is already very low, accessory mode won't drain the battery. It only stays on for 10 or 15 minutes specifically to avoid doing so.
If you do a lot of short trips so the battery doesn't have time to even recharge from starting the car, then it's going to be low to begin with.
If you do a lot of short trips so the battery doesn't have time to even recharge from starting the car, then it's going to be low to begin with.