I also have this issue.... it's frustrating.. but my story is a bit different. I got a used iPhone 4S which is bought in December, so it's practically new and I have no papers on it or anything because the original owner lost it...
The phone were locked and of course got unlocked, and I could use it fine. I had a fine connection to my carrier, could do 3G, send messages, receive them and make calls and receive those as well. But then after 3 days of a restored iPhone 4S, No Service appeared. I of course just restarted my phone a couple of times, and it eventually started working. Then the next day it wen't completely off, I just couldn't get a signal.
I tried every single solution. Restored, complete restore, replacing sim, flight mode... every single option mentioned on the entire Apple forum! But of course, some of us guys are unlucky and it still hasn't fixed the problem! The way I can get a signal again is by reinserting my sim card like a thousand times when it's turned on, and then sometimes I get a signal for 2 secs and then it goes to 1 bar and on to No Service. But I keep inserting it, and eventually it'll catch the signal.
Once I have caught this signal and it stays there, it usually won't go off (haven't experienced it yet) until I turn my phone off or enable flight mode. So my signal is great and I can send messages and receive them... but not I can't make calls or receive them! When I call someone, what I see is an immediate message saying "Call Ended".. and when people try to call me, they hear my answering tone or whatever it's called. And that's the first thing they hear, they don't hear it trying to call me, it just switches over to my answering tone like the phone is turned off.
I hope this is a software problem. If anyone knows if Apple is doing something about this, please let me or us know! I hate this... oh and by the way, I got an iPhone 4S 16GB 5.0.1 (9A406)