I'm not having any luck here at all...
What brand router do you have?
Try to adjust both bands to their strongest perspective channels. I had the same issue with my new router and this did the trick. I also used WPS to connect too.
Thanks a bunch. I think it's working now. I actually used the wps push button method. My wifi problems was when my s3 was connected to my Netgear router and I leave my phone idle for let's say 5-10mins. I go to pick up the phone and use the Internet on the phone it says I am connected to my wifi but it takes 30secs-1min for the Internet to kick in. The phone would also at various times drop my whole wifi network. But my wife's Rezound would not have any problems. Seems like your method has work. I left the phone idle for 10mins right now and when I went to use the Internet it immediately connected to the Internet. As before it would take 30sec-1min. I'll keep you updated on how things are going. Thank you so much.
After the ICS update the wifi on my phone would NOT stay connected. I apologize if someone has already pointed out that you need to do a factory reset after the update. It was the answer! I had tried all the obvious and not so obvious solutions mentioned throughout this forum and others. Back-up and perform a factory reset on your phone; it was easy & painless. The how-to perform a factory reset is mentioned within this forum and on YouTube.
Hope the info is helpful.