So drop by one of those, ask them to 'check and charge your battery' and expect it might take an hour or so. They hook it up to a charger, and that charger can tell how much charge the battery can hold and all. So here's the good news! They can check your battery at a car parts store like O'reilly or AutoZone. But the door does activate the lights, and there's like twenty of those, so they could add up to drain the battery enough to matter. It only uses juice while opening or closing.
The door isn't directly draining the battery.