I have tried everything, including advice from Apple On-Line Support. Just after I installed the original iOS8, they suggested wiping the iPad, starting from scratch with a factory default iOS install, and then re-installing from a back-up. Initially, the "No SIM" message disappeared, but after doing the re-install of my configuration it is back again. They also suggesting doing a re-install from the Cloud rather than iTunes, because that would force iOS8 compliant apps to be installed, rather than some non-iOS 8 compliant apps that can cause issues (seemingly there were quite a few...). That didn't work. Worse still under 8.02 it was intermittent. Now with iOS8.1 it is showing "No SIM" all of the time.
This is clearly a software issue - why else would it work/not-work when updating/re-installing iOS?
I have just wasted another half day wiping and re-installing iOS8.1 to see if the issue went away with yet another clean install (no apps). Nope - the problem is STILL there.
I sincerely hope Apple is reviewing these threads and will issue a fix soon. In meantime, I think we are all wasting our time trying countless "try this" suggestions to see if the issue can be fixed. I do not want to disable the cellular function on my iPad - that is not a fix. I need the cellular function to work. I am now relegated to using my tiny iPhone 5 screen instead.
This is clearly a deep rooted bug that Apple needs to be aware of and fix. I have an iPad that is now "not fit for the purpose for which it was intended" - a legal term which means that Apple needs to fix it, or I want my money back.