My Problem Detailed
I have been having this same problem for months. To be more specific, it happens whether I'm on 3G or WiFi. Back before iOS5 when I was on 3G, I could simply turn off 3G and turn it back on, but now with iOS 5, it is turning Airplane Mode on/off only, which like everyone else fixes the problem only temporarily.
Attempted Failed Solutions
It has transcended hardware and SIM cards. It was happening on my iPhone 4 and when I moved to the 4s, it was still there. So, it's most likely not the phone itself. I also swapped out SIM cards. That also didn't do the trick. That leaves me to one last idea...
Last Possible Solution
It's gotta be the software. Some app or process is hacking away at the connection, possibly hogging all of the connection. This was the Apple Store's original guess too (before I upgraded phones or swapped SIM cards). Their recommendation is to restore the phone with the base OS and not from backup. Then without adding any apps, make sure that it works fine (for possibly a day or two). Then start adding apps back one at a time. Has anyone tried this yet? With so much setup, I am hesitant to try this without knowing if it will solve it.
Alternative Solutions
If it is software, possibly we all have a common app/process that few have. Maybe we can all compare what we have. Unfortunately, my app count is still over 100 even after deleting more than half of my apps. Does anyone else have any ideas? I'd love to figure this out as it is extremely frustrating as you all know.