IPhone 4S. Suddenly started getting this problem, a LONG time after installing the latest updates to IOS7 (have also had this phone since it came out, so well out of warranty). Tried everything described by previous correspondents, nothing worked.
Decided to review my networks and I have two in my house. One is the usual one I use, and another is the default network that came with the router. Changed the security settings on the default network to WPA only, and my iPhone jumped back into life on my usual network. Definitely would not have wanted to put my main usual network on to WEP to solve this.
I think this is a conflict/handshake issue with individual iPhone configurations (my wife's 4S has not had this issue....yet), and having two networks in my house, both on WPA2, was definitely causing the problem, all working fine now.
Interestingly, since doing this, the 'cooking' effect my iPhone was experiencing for some weeks has gone as well, so no need to put it in the fridge!
Not saying this will work for anyone else, and obviously if your antenna is actually broken this will not help, but if it does work for you please let this feed know.
Tony