If the battery is out of the fob that long, won't it "forget" its programming?
The programming is in the car, not in the fob. The car is programmed to accept input from particular fobs.
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Interesting note, At first I tried to unlock the car with the unpowered fob but I could not find the "special spot" near the passenger wiper that is supposed to sense the key in the event of a battery failure.
The special spot won't work with a totally dead fob. It's just near the transceiver so that a fob with a weak battery will be able to access it. Remove the battery and you can't use the fob at all. If you could, there would be a slot to insert it as there is on the Prius (inside the car).