Key just stopped working..

Have you tried changing the battery? If so then have you tried the reset procedure described in the handbook? There is a link below if you don't have one, it's section 2.36 that describes how to do it

http://lee69.co.uk/Car stuff/Leon/Seat Leon 1M Manual.pdf

You need the original spare key, with the transponder inside to do it. The fact that the alarm is going off would make me think that maybe the one you have is just a spare someone has had cut and it hasn't got the needed transponder inside.

It could be that the module inside the drivers door has failed, sometime that causes the key not to work..... It's hard to say really. The best bet is to get it scanned with VCDS as that can read fault codes from the alarm and central locking.

Link to VCDS here http://www.ross-tech.com/

And UK distributor of the latest version. https://www.gendan.co.uk/product_VCV23.html (You will need a windows 7, or later, laptop to run it)

I would guess that the remote part is failing, changing the battery would normally solve the problem and wouldn't need the remote to be re-synced. I just had the same thing happen where I suspected the battery was going flat even though the led would illuminate, after changing the battery it still wouldn't work. I got a replacement on ebay and had to remove the old fob in VAG-COM and then add the new fob.
If you don't have access to VAG-COM/VCDS then your cheapest option may be to send off the remote fob for repair.

There is a process to add a key using the master key, someone has posted the process on the forum, but I don't think it can be removed without VAG-COM/VCDS. When my fob stopped working I used VAG-COM to remove the fob from the ECU (Block 45 Cent conv) and then added the new one. If you are convinced that your fob works properly then it would be the same process of removing and then re-adding the fob.

That is definitely the original second key. That code on it, the bottom part, that's the PIN that you will need if adding a new key with vcds.