The FC12 has an internal ribbon cable connecting its motherboard to each of the four quadrants of its switches, i.e., one ribbon cable powers switches 1 through 3, another powers switches 4 through 6, etc. I think you should open the unit, detach and reattach those cables, and apply hot glue to keep them in place. It sounds like they're just loosening on their own.
I ended up doing extensive troubleshooting with my unit because the upper left switch stopped working, but I learned a lot about how the unit works. In my troubleshooting, I would just try one thing, put it back together with the screws off to test, then quickly dissemble if I hadn't fixed the problem. With your unit I can almost certainly say you just need hot glue to make sure the internal ribbon powering buttons 4 through 6 is coming unseated every time you reassemble the unit. From what I've read, I don't think early FC12s were shipped with hot glue, but later ones were, to prevent this issue. Hot glue guns are inexpensive and easy to find; it's really a quick and effective solution. Sorry you're having trouble, but I'd give that a try before sending the unit in and waiting, because that might be just the repair FAS might perform on your unit!