This is happening with my new iPad Air and the replacement iPad Air. It did not occur at all with the iPad 2 I had.
I have had too many calls and chats with Apple on this iPad Air issue. And have been to the store twice: once to wipe the iPad Air (no restore, started like new with no content); the second trip to get a swap out. I've asked each of the MANY Apple reps if this is a known issue and they say 'no'. I tell them they should read their forums here, and the response I got was that this is for customers to help other customers and that the info you find here is not necessarily accurate. In short, they don't use these forums for much of anything (like customer insight), if they look at them at all.
I have more frequent shut downs since the 7.06 install, and have had other apps (like Pandora) lock up the device. I switched to Chrome a few days ago and things seem better (plus when the browser does crash it restores all open tabs which is nice).
I have very few apps and data on the device since we did not pull down the iCloud backup. So, Apple can't say there is a corrupt backup causing it. They've tried to pin this on that and then on the hardware (thus, the swap).
They also ran diagnostics and through the results, suggested that Google Drive (app) is causing the crash. I suggested if that really is the case, they should take that app off the AppStore until the issue is resolved. I'm running "Drive-less" and the crashes and lockups continue.