FWIW, I also heard that if you store your fob within a certain distance of your vehicle, like on the wall next to the door to the garage, that it will be using battery power as it communicates with the vehicle even through obstacles. In that case, it might be worth trying to leave your fob further away from the vehicle.
It's also a good way to have your vehicle broken into or stolen.
It's a known fact now that thieves can intercept the signal going from your fob (that's in the house) to your car,
boost the signal so that the car thinks the fob is right there, and then simply open the door and drive it away.
There are lots of stories of high end cars being stolen that way.
They end up in a shipping container and are headed to the middle east before you even report the loss to the police.
Quote from an article on a Canadian news site:
According to Markham automotive security specialist Jeff Bates, owner of Lockdown Security, wireless key fobs have a role to play in many recent car thefts, with thieves intercepting and rerouting their signals -- even from inside homes -- to open and steal cars. According to Bates, many of these thieves are using a method called "relay theft." Key fobs are constantly broadcasting a signal that communicates with a specific vehicle, he said, and when it comes into a close enough range, the vehicle will open and start. The thief will bring a device close to the home's door, close to where most keys are sitting, to boost the fob's signal. They leave another device near the vehicle, which receives the signal and opens the car. Many people don't realize it, Bates said, but the thieves don't need the fob in the car to drive it away.
Bates says, if you have a key fob that can wirelessly unlock/start your car, you should not keep it by the front door.
"If you do live in a house, try to leave your keys either upstairs or ... as far away from the vehicle as possible," he said. "The other thing that you can do is there are products out there that you can put your key fob into," such as a faraday cage -- a box used to block radio signals -- a key pouch, which works similarly, or even a steel box.
Food for thought.