Having similar issues. I have been struggling with the data connection on my iPhone 4s for over a month. I am in a rural area of West Michigan and am using AT&T. I purchased the phone during the first week that they were available and everything was fine until about the 20th of December. I had stopped using wireless at all because Siri would fail when trying to authenticate on my work network which is available all over the small town where I work. My AT&T Data plan is unlimited ( funny or sad?) so just staying connected on 3G all the time and having Siri ready to go was working fine.
Then I lost data at home; nowhere else, just at home. I can drive a circle around my house and get full connectivity; worse is that I always have 4 - 5 bars and 3G and I can see the AT&T Tower 2 miles out my dining room window. We have 3G, 3GS, 4, and 4s phones; the 3G and 3GS are able to use cellular data almost anytime. The 4 has been intermittent and since Dec 20 I have had about a week of data that would work after cycling airplane mode on and off and about a week of perfectly normal operation. I would guess that all total I have had 45 days of perfectly normal cellular data operation on my 4s. If I leave home everything is fine, no complaints. Right now it will connect for 1 minute if I cycle the power on the phone; it will reconnect to cellular data as many times as you would care to cycle power.
What I have done:
Reset the network settings.
Called AT&T and had them troubleshoot and re-register the phone on the network.
Replaced the SIM
Replaced the Phone
Completed 3 service tickets with AT&T with various levels of temporary success. (The last on worked for two days after they called to confirm it had been corrected)
I have wiped and restored the phone from an iCloud backup, from a computer backup, and as a completely new iPhone with no additional applications or data. Nothing- No Change
I have cycled off everything in my house ( routers, server, PC's, Wii, Dish....anything that creates or receives a signal). Cycled the phone off removed and re-inserted the SIM, reset network settings in the phone.
This feels very much like an interference issue but I cannot sort it out, neither can AT&T/Apple. If it was not interference it would occasionally connect.. We need some help; without the 3G and Siri at home (where I work a couple of days a week) I would be just as well off with my old iPhone and the extra cash.