I'd like to add my voice to the list of people having this problem. However, to note, I'm on my second iPhone 4s as the first one I had, had a stuck pixel and I got it replaced. The first iPhone 4s had NO wifi problems - I could stay connected to any WiFi and it would be instantly ready whenever I asked it. The second iPhone 4s I got, I noticed that after a few minutes (or even seconds), on WiFi, the phone would be sitting trying to load things as if it lost internet connection. At first I dismissed this but as time went on, I noticed this was really starting to be a problem. And confirmed, my iPhone 4s loses WiFi sometimes instantly or sometimes after exactly 10 mins (watching Netflix).
I've read through this entire thread and tried a hard reset (of settings), static IP addresses (I'm a software developer with a lifelong history of IT), using GoogleDNS/OpenDNS, and turning off WiFi sync in iTunes. All of this was a temporary fix as the problem came back.
I know it isn't the router. Why? My first iPhone 4s worked 14 days flawlessly on it (before I recognized the stuck pixel and replaced it). Now... I kinda wish I had that stuck pixel because I can't use WiFi reliably. Sad!