I think a good voltage tester will tell you if there is a constant draw on the battery terminals, keeping in mind that you should expect some draw because the fob is always emitting a signal, which allows entry to the car by touch.
A few years ago I though that my Mustang's key fob was always quick to need a battery. Then I realized it only happened near the grocery store. Something in that location was preventing the signal from transmitting. Could that be the case?