I know this is a long shot, but physical problems are so rare, that many of us usually don't account for them. What I'm getting at is that it is possible the ALT key on your keyboard isn't working properly.
Maybe you are pressing the key and keeping it down (which should register as a single continous key press) for when you press TAB. There may be a short of some kind that makes the keyboard register multiple ALT key presses instead of a single continous one, which is what is required for ALT+TAB to work.
Like I said, it's a long shot, but try temporarily using a different keyboard to see of the problem goes away. If the dissapearing act of ALT+TAB remains, then try Brink's solution of running a system file check using SFC /SCANNOW.
If that doesn't work, then it is possible that some application you are running is hijacking the keyboard, or trying to force itself into the foregound, regardless of what you do with ALT+TAB. Try running a full virus/malware scan.
