It's not the fob, it's the car.
The alarm consists of the remote (transmitter) and the alarm module under the driver's seat (receiver).
In order to reduce power consumption and save the car battery, the alarm module (receiver) stops listening for the remote after 120 Hrs. (5 days).
Once you unlock and start the car w/ the key, the whole system wakes up again and the remote will now be recognized by the alarm module.
