I have been having this problem for about a month already. I've tried everything that's been suggested here: I changed my SIM card, installed the latest build (9A406) of iOS 5.0.1, but the problem is still there.
The phone loses network all the time displaying "no service". The only way to get it back is to try to make a call and after the call fails it starts searching and after a while catches the network. Then I can make some calls and after 10-15 minutes it drops the network again and the process repeats itself.
It's VERY frustrating indeed. I bought the phone in Rome in November and for a month it seemed to work fine and then the problem started. Sometimes it displays "SIM failure" and I have to restart it to get it to work. I'm not sure if it started after I upgraded to 5.0.1, and do hope it's a software issue.
If after 5.1 the problem isn't fixed, it's suely going to be my last phone from Apple, which is very sad, since I've had three iPhones and this 4S is the worst phone I have evere had.