Reporting back since I have now received my Chinese remote key fob and would like to have some insights if possible.

So afterall, I was unable to pair the new remote key fob with the car, which makes me believe the issue is in the car itself and the keys can be ruled out. Quick recap of the situation:

-I have two original keys for the car which both I have been able to pair with the car.
-Currently only one is paired.
-The remote door locking/unlocking and remote trunk opening only works intermittently, lets say 5-10 % of the times when pressing the buttons. Although sometimes it feels it doesn't matter how many times you press the buttons it just doesn't work and you are forced to unlock or lock the door lock manually.
-When I got the car last August, the other remote fob was working perfectly, the other didn't, perhaps it wasn't paired with the car. Then after few months it began to show issues, first only every now and then but eventually got to this point. I don't think it has gotten any worse in the last few months.
-Both keys have been checked by a company which specializes in car keys and according to them, should be fine now. The batteries were fine in both of the keys, but the other one wasn't sending a signal at first but this was fixed after adding some solder.
-Central locking button inside the car is working perfectly

I guess it is still somewhat possible that the issue is in the keys and maybe the Chinese key fob is just faulty to begin with but I really think I should now start investigating the car itself. Is there a receiver somewhere which could be checked or maybe the wiring?

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09/2003 X5 3.0i
02/2003 X5 4.6is (non-runner)