FIXED!!!!
I have iPhone 4s running 6.1.2 Everything worked great before the lovely update. My wifi did the same thing that everyone else's seems to be doing. It would not recognize my home router.
Evidently, in the update, Apple changed how the "Ask to Join Networks" button operates. Previously, I didn't have to have the button toggled to on, my phone would just automatically lock onto my router. I have fought and fought with this update. I have done several "network settings resets". I have even restored my phone twice. I have tried every crackpot, and not so crackpot, suggestion on these forums and NOTHING has worked. I could go to settings and connect to the router each time I used the phone, but it would only stay connected for a few minutes.
Today, I toggled the "Ask to Join Networks" button to "on", then opened Safari. My phone then asked if I wanted to join the network, I responded with "join". My phone has been on wifi all day! I left home and came back several hours later, and FINALLY... my phone locks on automatically.
Go to settings>, Wi-Fi>, toggle "Ask to Join Networks" button to "on". Then click on your router/network in the list.
I realize that everyone's problems are not the exact problems I had, but maybe this will help some of you having problems.
Good Luck!