Well, hell. That is just odd. I do know that FF14 has issues with dropping (wireless) controllers, but I've not heard any issues with wired controllers until now. First thing to do, hit up Microsoft Hardware and make sure you have the newest drivers. If that doesn't work, try the standard "This will fix everything when nothing else works fix..."

In your Documents / My Games folder will be a folder for Final Fantasy XIV. Create a folder on your desktop. Move everything in the FF folder into the temp folder on your desktop. Move only the Users folder back into the Final Fantasy folder.

I don't know if this will actually work. I expect it won't, but this "fix" has fixed some of the most random and bizarre bugs in the game, ranging from UI/Widget, to disconnects, to graphics glitches. Here's hoping?