+1
The lithium batteries used in remotes have something like a 10 year shelf life, and should be good for at least 3 year in a regularly-used remote.
When out of range of the vehicle, the transmitter is not pulling power, unless it is near another device that would cause it to "wake up"
Cell phones and computers may trigger it to transmit the serial number, but there is no definitive list.
Generally, when battery life is that low, it can be traced to storing the battery at home within range of the vehicle (a lot of people drop their keys in a tray in the garage as they go through the interior door), which causes the fob to actively transmit constantly, or tightly fitting pants that randomly press the remote buttons.
But in your case, neither of these is true.
If the dealer you bought from stores the keys in a lockbox clipped onto a window, then it's possible the fob was picking up the signal from the car and transmitting on the lot 24/7. I've done a few test drives at Carmax, and every car that had a smart key had a dead battery because of this. Our Toyota dealers keep the keys in a vault inside the showroom and check them out to the salesman for test drives, but used car lots generally use lockboxes on the cars.
Putting the fob into the Altoids tin is not doing anything helpful if you have put the fob into battery save mode... in that mode, the fob is not "listening" for a wake-up signal unless and until one of the buttons is pressed. Putting it into battery save mode is similar to removing the battery.
The Altoids tin is a really good idea if you park in a garage where the car may be in range of the fob inside the house.