My troop loyalty went down by itself in RoC, what can I do?

It will depend on which type of RoC you are in. If it is total war then most likely an enemy has destroyed one of your honor buildings. You can replace it and repair it to get the loyalty back.

Or a building may have been recalled if an alliance center has been moved.

If not then have you recently changed your Specialty points and removed some from the Blue section to the right?