Update: I got one of my D700 bodies back, with a new hot shoe. It is DEFINITELY tighter and the SB-800 more rigid than on the one that has had problems again. But... try this before you send the camera off:
-- Clean the contacts ob both the camer hot shoe and the flash. -- Mount the flash on the camera. If it is loose, gently press it backward , and if it resumes functioning correctly, the issue is a loose or "sloppy-loose" hot shoe. Before you spend $200+, I'd be inclined to try the water guard recommended elsewhere in this thread and or go to a flash bracket and connection to the hot shoe. That puts less stress on the camera hot shoe and reduced red eye substantially. I don't recommend trying to bend the hotshoe closed a little, as some have done. There are parts under it and dinging them is a distinct possibility -- probability in my clumsy case!
I am NOT a camera repairman -- but this worked for me. I am now more convinced than ever, that the D700 hot shoe is NOT strong enough to take the use many of us subject it to when using Nikon flashes. It seems to "open up" under use, causing insufficient contact with the contacts and thus, disabling communication between the flash and camera.