Originally Posted by HammFist
Well, the fob has to respond to RF signals from the Jeep, or it wouldn't work.
Yes, but it does so with an RFID chip, like the theft detection chip glued to items at a retail store. It doesn't use the battery; it's powered by the energy of the transmission.
As far as I can tell, the fob only draws on the battery when you press a button. Then it originates a transmission with a much stronger field than RFID. That's why you can remote start from a hundred feet away but must be within five feet for passive entry.