Duck tape it for cheap easy solution if the tape leaves behind a sticky residue you might goo gone it as long as it doesn't touch the non plastic part, not sure how the chemicals would react. Duck tape is a strong tape.
You could get masking tape and just wrap it around a few times not sure how that would affect the controls though. I doubt it would fall apart if you wrapped it and overlapped the tape. this tape is less sticky and most likely wont leave behind something sticky when you peel it off
tape is the only thing i can think of that does not require any fancy moves.. My cell phone has the same problem when I pick it up it falls apart.
Is the toy designed so that if the back falls off it does not work? that would be kinda stupid especially if its a common problem which sounds like it is to rabbit vibes