If the rook doesn't take, then 21. ... Nc2 fork.
Non-resigning computers

It's the user-interface, not the engine, that decides when to resign. Fritz, Aquarium, and Arena all let you configure the resignation point.

I couldn't find the option in my Rybka/WinBoard combination (downloaded from here: http://www.chess.com/download/view/portable-winboardx--rybka-22---updated-setup)
It's a real pain when I'm trying to practice some endgame positions (like K+B+B vs K or K+B+N vs K or some King and Pawn endgames) and the engine keeps resigning....
Does anyone know where to turn it off in WinBoard?

I got a resignation out of my Novag Obsidian just the other night (it was set on a level that has roughly the same strength as a novice after a three-martini lunch). I think it's a nice feature although not essential. Gives it a bit of a human touch, and if you want to, you can force the computer to play on to the bitter end.
We all know that there are few, if any, computers out there that will opt to resign rather than play out a hoplessly lost game to the finish. The following is a game between my Excalibur chess station (on its highest level setting) and one of chessmaster 8000's personalities:
So, does anyone know why 21.Rxe1?
And when would you have resigned?