I've just found, and fixed, an interesting fault on one of these key fobs.
Several of the solder joints on the SO-8 IC had cracked, leading to very intermittent operation. I guess that the board is just a bit too flexible, and the joints get too stressed. Anyhow, resoldered them all the key works fine.
You are so lucky.
I did that on my (not a Jaguar) and it lasted 6 months. Then soldered it again. If you can keep pushing off death 6 months at a time …...
If you push the buttons softly it will last longer. Some people think that the fob will transmit farther if you push harder.
I see a lot of bad remotes in my line of work. Most oem remote failures are from moisture getting in and causing some type of havoc. Gm's are famous for the small caps deteriorating. Aftermarket is typically always just poor components and bad solder joints. Especially at the battery holders. Can't say I have seen to many with the ic having bad joints so hopefully it will hold up for you with no problems. The oem jag remotes are built pretty well.
Jag were part of Ford when the X-type was made.
Not any more.
Previously the MINI, Rover 75 and Landrover Freelander all shared the same key fob type, made by Valeo. That was when BMW owned them all. Now Jaguar Landrover is owned by Tata, the Indian company.