I am only five years late to comment on this
But out of curiosity, have you managed to sort this out?
I have the same car V4 T4 2001, used the fob today as always jumped in the car with the family and spend the day in London, when I finished I drove back to Coventry, parked the car, tried to use the fob to lock as always but it was total silence!! nothing at all! I used the key to lock it but the alarm is not armed! the fob itself is working fine and the battery is brand new.
I wonder if you guys managed to find a way out of this other than re-programming a new fob or buying a new one from the dealer.
Thanks much