I have a 1995 518I with a 3t alarm (single button on three inch long
fob) and over the last few days have had to get closer and closer to
the car before the remote will open the doors. Now it's stopped working
altogether.

The obvious starting point was the battery in the fob so I changed this
but still no joy. I then tried the spare fob which worked the other day
but still nothing.

The car starts and runs fine apart from that so could someone please tell me if this is a common fault and how can I rectify it?