I can't help, other than to say my Fuze v1 does the same thing--I thought it was just my beat-up Fuze developing a hardware glitch. I don't sync, I just copy tracks using a file browser, but I do have a consistent problem with the Fuze just powering down as files copy. This of course screws up the copy, Windows Explorer freezes and soon I get the "File not found" error because of the premature unmount.
Don't know why this happens. It could just be a Fuze v1 thing, because my late v2 never did it.
Edit: I read somewhere else on the forum that something happened after Rockbox v3.9 to make the USB act a little off. Try replacing your current build with 3.9 until they get it sorted. Hope that helps!