I just brought my iPhone 4S into an Apple store last week because the top button was not working, they gave me a replacement phone that seemed to work. Please note, I have Verizon as a carrier. However after updating to ios 6 last week I travelled to San Francisco. On my way there (I took a train to NYC for the flight and noticed this on the trip) I began noticing that the network was working perfectly but would then just cut out and show it "searching" while a person I was travelling with using an iPhone 4S running ios5 was maintaining 3G connection, also using Verizon. This happened a few times on the way and again once I was there, maybe 10 times total between Thursday and Saturday morning. Then this past Saturday morning, I was using the phone, connected to 3G and browsing facebook, again it dropped the connection and began "searching" for the network, this time however it never reconnected, it just searched for 8 hours. During that time I:
1) Turned on and off airplane mode
2) Powered off and on the phone
3) Soft reset it
4) Reset Network settings
5) Reset all settings
None of these things helped, each time the phone just sat searching. Finally I created a backup to iCloud over Wi-Fi, and erased the phone. Upon booting up it could not activate for about an hour, and kept telling me it could not connect to the cellular network. Finally, it was able to setup and I pulled back down the backup from the cloud.
The phone then worked, but was cutting out from strong 3G connection to "searching" constantly, as in it would connect to 3G for about a minute at full bars, then drop to no 3G with 1 bar for about 10 seconds, then searching for about 2 minutes. It would cycle through this all day. I then flew back to the east coast yesterday. Upon arriving in NYC and taking my train home, the entire 3 hour ride was cycling as noted above, full 3G -> no 3G and 1 bar -> searching. All the while my co traveler had no issues again. Now that I am back home, the connection has gone back to pretty consistent, dropping about twice last night and 3 times so far today. I have no confidence that this will not happen again and do not know if it is an issue with getting a bum refurb as a replacement that has antenna issues, or if it is software related since it seems a few others have been having the same issue as seen here and also in this thread: https://discussions.apple.com/thread/4336440