Here is my recommendation.
If you have not updated to iOS 6.1, do it. It launched yesterday. I did not have issues with my iPad 2 using iOS 6, but my iPhone 4S had major issues with iOS 6.0.1 and 6 when connected to my Netgear DGN1000, but only when using WPA2. My Apple TV 2 had similar issues as well.
The update to iOS 6.1 has corrected the issues I experienced with my 4S using iOS 6 and 6.0.1.
Once updated go and reset your network settings and connect to the router again.
I am telling you... I attempted everything when connecting using WPA2 on my Netgear prior to iOS 6.1. Nothing worked, I gave the 4S its own IP on the router you name it I attempted it. The only setting that would work on the Netgear prior to iOS 6.1 was WPA and WEP. I even experienced issues using mixed WPA and WPA2.
If the update to 6.1 and resetting your network setting on your device does not work. Help yourself out and go to http://www.apple.com/feedback/
Provide honest feedback, your device, iOS. Your router name, model, settings such as WEP, WPA, WPA2 etc. Also provide what you have experienced, which applications are causing issues etc. The big issues I encountered with my 4S was the inability on my Netgear to connect to the Updates section of the App Store and the native iPhone Weather app. With my A TV2 I could not connect to Netflix using the Netgear WPA2 encryption.
I updated both last night and they work perfect thus far.