No, I have iPhone 4S and whit iOS 5.1.1 the wifi worked also in standby. I have the problem with iOS 6, so I think that it is a software problem.
I had the same issue with all my apple mobile devices. I had tried all the solutions from applecare but none of them works for me. Finally, I called Bright House(my ISP). And, they came and replaced the Mode and wifi router. Then, everything just goes fine. For my situation, I would say the problem should be the old WiFi router! But, I still have an question. Why does iOS5 work just fine with the old router, not the iOS6? Anyway, I got everything working right now with the new router.