No extra settings for the remote and apps it should work and is not a problem I have seen reported before.
Have you tried factory resetting the remote and repairing.
Press and hold the TV and Rewind button for 10 seconds which will factory reset the 360 remote.
After the factory reset, try pressing TV and 0 button for 10 seconds and it should now force pairing.
If that doesn't work you could try a factory reset of the 360.
It's only a partial system reset and not a complete factory reset. You are given 2 options,
Choosing Keep Recordings, means you won't lose your recordings and any planned recordings or series links you've set up, but you will have to sign into your apps such as iPlayer, Prime, Netflix and ITVX again, also Match frame rate and Standby power consumption will go back to their default settings if you have changed them.