I have the same problem.
I have had the iPhone 4S since March and updated it to iOS6 OTA in September, I believe. The wifi worked fine until 2 days ago. I think I updated it to iOS6.01 too OTA, but about a week ago a dropped it. Nothing broke, and the wifi worked fine after but just two days ago the wifi stopped working. I tried the "switching to airplane mode then hard restart, then turning airplane mode off and turning the wifi on" and that worked for a little while. I tried that 3 times and it all worked, but wifi was lost shortly after connecting each time. Now my wifi button is greyed out. I also tried letting it die and recharging it, but it doesn't work. I don't know whether this is because of the update, or because I dropped it. I don't think it is because I dropped it, because nothing shattered, and the wifi worked fine for days after that. It's only recently where my wifi did not work.
I am very upset, because I use my phone a lot at home too and the wifi makes browsing a lot faster and easier, plus it preserves the battery too.
My battery runs out very quickly now, in 1 hour I lost 20% without touching it at all.
My battery could have lasted the whole day without touching it before, and it would have been at 94% or higher.
I called Apple yesterday, but since I did not have a warranty, they could not do anything about it. Which I find is very stupid and useless, you pay so much for a phone, a high quality one too, and they expect you to pay even more for insurance? The insurance isn't cheap, either. This is really unfair because many people have the same problem too. 347,042 views and 2,508 replies on the largest thread about this issue.
I expected a lot better from Apple.
We need to continue posting about this until it gets brought up into their attention even more. Apple NEEDS to fix this as soon as possible for all of us.