Same thing happened to me a few weeks ago. My 11 month old XT-1 lost all four screws -- I assume gradually over the past year, as it's nothing that I check each time I clean the camera.
Fuji Repair in NJ fixed it at no charge. Took about a week.
I use BlackRapid camera and wrist straps, and I've changed my tripod plates to include a BlackRapid attachment point. I'm thinking that putting these on/off the camera have been giving the screws a chance to loosen and fall out.
I'll be checking more often going forward.
