Update:
while led waiting for 8.1 I decided to to a total reset on 8.0.2. I set the iPad up as a New IPad as I expected a backup/restore might bring the problem back. (I used the CopyTrans program to save my photos, messages etc so I could load these back up afterwards without bringing back some corrupt settings). While the problem persisted after the erase and re-config, it was definitely an improvement. I only experienced No Service 3 times in six days, rather than the 3 or 4 times a day I had beforehand. I also found that by going to Settings/iCloud - in portrait mode only! - caused the device to search for service and reconnect to my carrier. (I hadn't yet restored anything from my CopyTrans save, so it was a bare-bones Apple 'New iPad' with no contamination).
I Have now upgraded to 8.1 and after 36 hours I have not had the problem. So, 8.1 is looking good for me. I hope others have as much success.
WHy why can't Apple just communicate with its customers, acknowledge issues and let us know it is working on a solution? Saying nothing and not admitting to faults just gives a usually great company a sinister uncaring appearance. Nothing in this world is perfect every time. I expect bugs with new products and releases, and would be tolerant of reasonable delays in getting a fix - if Apple would just own up and communicate its remedial plans. (End of rant!)