Last few days the door locking system is not working - I press the fob and she makes a sound like the relays are clicking but the locks don’t actually lock. It’s like they just don’t have the power necessary to do so (?) A second press and I get a chirp, but no other sound at all. A third press then yields a chirp and headlights come on, but nothing else. If I then open a door the escalating alarm sound starts to begin but shuts off as soon as I press the fob. 
A few days before this all started when I hit the fob the door locks rapidly started locking and unlocking, like the system couldn’t make up its mind which to do. Also, sometimes one door would be locked and the other unlocked. When I manually put them back in synch with each other (which sometimes was difficult, using finger pressure) then the system would work normally for awhile. Once though I couldn’t even get the passenger door to unlock with the key. 
Change the car battery.
When this starts happening to my car, it ends up being about 6 months before the car randomly won’t start and needs to be jumped.
Hmmm. The battery is relatively new, though. Although I am wondering if the belt slippage at start up means it isn’t getting charged up like it should. Seems like my lights are a bit dimmer of late than they should be. 
Thanks, VK.
Yeah, that’ll do it.
This sometimes happens on my X300, I just press the central locking switch on the centre consul and it seems to clear the problem. Of course you may not have a CL switch on the XJS, I’ve never been in one so I don’t know…
I’m going through the same thing right now. My alarm system and door locks is very dependent on a correct battery charge. I Drive the car about every 10 days and the battery always needs either a slight charge or a long charge if I go over 10 days.
If the battery goes flat, almost nothing will work correctly. Once charged, the car operates like it was new. I’m looking into a battery tender to try and head off massive system failures.
Gordon
If the problem is not a weak battery, one of the doors may not be getting closed properly.
The worst thing I had was someone closed the door lightly.
I had to get in the opposite side, push the paddle hard, and give the door a massive push to open, all at the same time.
It’s a little easier if the window is open.
Then you can hold the paddle to unlock while pulling the door.
Also, I’m not using my battery tender any more, so let me know by PM.