Exactly the same issue here! Upgraded to iOS8 per the recommendation on the system/compatibility chart, and immediately was dropped to "No Service" on my cellular connection. I tried a full restart, and was able to reconnect for about 5 minutes before it disappeared again.
In attempting to contact Apple support through the website, I received a response that it would cost me $20 for them to speak with me because I'm out of warranty. This seems like a huge issue that a growing number of people are experiencing. I hope that there is an official response soon. Ugh!