The cable cover on Hori's excellent RAP sticks is quite fragile and it seems they're broken or missing more often than not. When I bought mine, it was still whole, so I immediately dropped it and broke the hinge post off.
Hori-Hinges.jpg
It took a few tries (above) but I managed to make a very simple and small wafer that replaces the outside hinge post. It requires only a 1.5mm square hole to be cut into the stick where the old post was, then it presses firmly into place.
Note: it goes in at a steep angle so that the post is flush with the metal cover, the other end is lower, to the top of the metal cover screw post. I don't think this is immediately obvious in the photo.
HoriHinge-1.2.jpg