On the Elite series 2, follow the ifixit guide located below until step 14...
[guide|158892|Xbox Elite Wireless Controller Series 2 Battery Replacement|new_window=true]
On the lower piece of the controller that contains the battery, locate the two small PCB parts each held on by two torx screws (T6 I think). Those are the boards that the paddle buttons are mounted to. Check to see if they are mounted correctly. Perhaps one of them is missing a screw or perhaps there is some debris interfering with the proper mount of the board or boards in question.