I have exactly the same problem. I upgraded my iphone 4 to ios 6 and intermittently can no longer text or make calls. I have restored the phone, reset network settings, restored as a new phone - all with the same problem. Yesterday I had an Apple Genius appointment and they did a DNS store - it seemed to work ok for a few hours and then stopped working again. I'm pretty sure this is an ios6 bug as my phone had no problems till the day I did the update.
One point - the problem is much worse when I have my wireless on at home or work, i.e. I can no longer ever text or make calls when wirelss is on, even when phone set to 3G only. However, if I switch modem off then phone works better but still not all the time. Very confusing, even the Apple guys weren't sure why it's happening. Can anyone else help???