2002 Volkswagen Jetta Passenger doors won't unlock with rem

Electrical problem
2002 Volkswagen Jetta 4 cyl Automatic

The passenger doors of my 2002 VW jetta stopped unlocking with the remote key. Clicking the remote key unlock button unlocks the front door and clicking it twice should (and used to) unlock the passenger doors -- but it doesn't anymore.

The passenger doors do unlock manually by turning the key in the door handle. And they also unlock when I use the button on the driver side to unlock all the doors.

I showed it to a mechanic who looked at the electric system and said everything looked ok and he couldn't figure out the problem. He said I would need to take it to the VW dealership. He said there's an internal transmitter for the passenger doors which may have stopped working. Does that sound like the problem? And if so, how much do you think it would cost to get it repaired (approx)? I'm trying to figure out whether it's worth taking it to the dealership to get it fixed.