My iPhone 4s wifi became "greyed out" about a week after updating to iOS 6.0.1. It's always worked perfectly, no problems, and nothing seemed to trigger the failure (no changes in software/firmware, hadn't synced or changed any settings, no extreme temperature changes and I hadn't dropped/damaged the handset in any way).
I researched the problem extensively, apparently this isn't an uncommon issue. I tried all the standard troubleshooting; reset, "hard reset", reset network settings, reset router, even did a full factory reset, nothing worked. I saw that other people in the forums have had success heating their phone up with a hair dryer and putting their phones in the freezer, ridiculous as that sounds. There's no Apple store anywhere near me, and I'm not eager to send my phone in to support by mail, so as a last resort I placed my phone in the freezer for 15 minutes. I can't endorse this method, because I'm sure it's not good for the phone and could potentially cause more damage to the battery & hardware. When I removed mine from the freezer, it showed the "connect to battery" icon on the screen (even though it had full battery when I put it in), then shut itself down. There was quite a bit of condensation beneath the screen, I dried it as best I could and powered it back up, and the wifi was working!! That was yesterday afternoon, and it's still working as of now. From what I understand, the phone's internal sensor mistakingly believes it's overheating, so it's shutting down the wifi (because wifi causes the phone's temperature to increase). Not sure why people aren't having the problem until after updating to iOS 6, but hopefully there's a firmware fix that Apple will release soon, since it appears to be a widespread issue.
Good luck!
Emily M.