This story has a happy ending and a few solutions.
This morning, when I put my week-old bumper-protected iPhone 4s with iOS 5.1 down on a hard counter, it rattled it a bit. The "NO SIM" message appeared immediately. I found various solutions on line and tried some. I also tried gently wiping the circuit side of the SIM card with a micro-fiber cloth. Nothing helped.
I scheduled a Genius Bar appointment at the Palo Alto Apple Store for later in the afternoon. While waiting, I backed up my data using iTunes. Knowing I might have to put my MicroSIM into an old Nokia candybar until I got the iPhone back, I stopped at a local repair shop (MobileKangaroo) to pick up a (free) MicroSIM-to-SIM adapter.
The Apple Store Genius who helped me took all of three minutes to fix the problem. He popped out the SIM tray, wiped the circuit side of the card not-so-gently on his shirt, and shot some compressed air into the tray and the slot. When he put the card and tray back in, it worked. He said if it had failed, he would have installed a different SIM to see if that one failed or worked.
It's been five hours since El Genius repaired it. No problems so far. He said if it happens again, go to AT&T. The phone may just need a new SIM.
I think what happened is that the rattling of the iPhone shook loose a tiny particle of conductive dust that had worked its way into the device during manufacturing. The shaking landed on the conductive side and caused a tiny short circuit.