Jag S-Type -intermitent fault where the remote fob does not work

This does not sound like a fob fault - but a locking control module fault , either in the hardware or software of the unit. Get it checked at a Jaguar dealers. When unlocking using the key - as soon as the door is opened you should hear a chime sounding inside the car - this is a timer counting down to sounding the alarm. If you put your key in the ignition as soon as you open the door the alarm should not go off and the chime should stop. If it does not this again points to a fault in the locking controller.
hope this helps - good luck.