I just figured out something - for those, who'd like to know more, I'll explain in detail below - for the others: Here's a spoiler:
Suddenly key would not start the X-Type anymore (it was my key number 4), and I found very quickly the reason: The transponder-pill inside of the key-fob had somehow "died" - I replaced it, and voilà...:

The picture above shows the transponder pill next to the key, which normally lives within the front part of the key-fob...

My advise number 1 is: Make copies of your OE keys! You should have received with your X-Type two ORIGINAL keys. If you should ever loose one of those two, you'll be buggered! This is why the first thing I always do about a new Jag is create a 3rd and 4th copy. Copying the REMOTE of an X-Type is quite simple, regardless how many keys you have to start with, but the key fob also contains (in the front part of the key-fob) a TRANSPONDER-pill or transponder-chip, and without that transponder, the car will not even attempt to start up. And to copy THIS TRANSPONDER, you'll need both ORIGINAL keys...

Normally, if you place the key into the ignition and turn it into position 3, you'll find that the red light in your centre console lights up red for an estimated 5 seconds, after which the red light will turn itself off again (at least on the 2001 X-Type, only which I had the issue at hand - I currently do not remember, if that thing about the red light is the same on newer X-Types).

But what I just experienced using my 4th key for the X-Type (which worked perfectly before): That red light did not turn itself off, but after those approx. 5 seconds it went into a continuous blinking mode - PLUS: turning the key from position 3 into START was to no avail, as the X-Type would not even attempt to start...

Now: My special situation was that I did not start THAT X-Type for about 1 year, I think, but I had the battery removed (before putting it back in for the occasion), but I was sure that the battery was doing just fine, as I has it sitting in the garage and I permanently recharged it with one of my CTEK chargers (15A).

Thus, if it's not the battery...: Why would the X-Type play possum? (meaning: why would it feign death)?
The only thing, which came to mind was the the transponder was "playing possum"...
Thus, I got my keys number 1 and number 2 (I have them all numbered) from the house: They were both starting the car/cat (and btw.: Perfect start at first attempt after about year, and it purrrred perfectly).

Thus, things were very clear now: The transponder-pill of key number 4 (which I self-programmed years ago - and I'll explain below, how), was non-operational.
The first logical conclusion would be that that pill somehow lost it's memory so to say - HOW such a transponder-pill works is an utter mystery to me...
Logically, I attempted to reprogram that transponder-pill AGAIN after all those years, but to no avail. It did not want to be programmed anymore.
Thus, I concluded that that transponder-pill had met it's maker (=is dead a a Dodo, it's now an "Ex-Pill/Parrot" (Monty Python)).
Luckily I do have a box with brand-new never before used Jaguar flip keys. I removed the transponder pill from one of those and put it into my key number 4, did the transponder-programming-ritual again, and key number 4 was good to go (no more blinking of the red light in the centre console, and that key could now also start the X-Type). The transponder pill in the picture above this THAT one, which is dead as a Dodo, but it does not look different than any other of those pills...
I do not have the foggiest, though, as to why this pill is dead, as I also have no idea, how it works in the first place...

And here as promised the programming ritual to DIY program a 3rd and 4th key for your X-Type, which works only, if you still have your ORIGINAL 2 keys, which is exactly why you should create a 3rd and 4th key, if you have not yet done so, and then only use the 3rd and 4th key to drive the X-Type and keep the 1st and 2nd in a save place at home...:

You simply insert the 1st ORIGINAL key into the ignition and turn it to position 3. Watch the red light in your centre console - The light should light up red (no blinking) and then simply turn itself off again after an estimated 5 seconds. This tells you that everything is alright with the key and it's transponder. Next you remove that key and insert the second ORIGINAL key, again into position 3, wail till the red light goes off (and does not blink) and then you remove that second key and insert the 3rd or 4th key (only one, then start from the beginning, if you have more keys), turn into position 3... - and : Finished. Now that additional key should start the X-Type just like the 2 ORIGINAL keys...

Note: I read on the net, that you should wait 30 seconds between keys - that is nonsense...