Apple support told me that they are aware of the problem in safari with ios 7/ipad air. They said "this is why we come out with ios updates". I said.... well, what are we waiting for? Wouldn't one think this is a bit more important than a "FaceTime issue", which was their reason for their ios 7.04 release.
Anyway before admitting this was a real issue, they gave me some suggestions....
Maybe some of these suggestions may work for someone out there, but they did not for me.....
First - They told me to clear my cache and cookies and it should help. For me, it did not.
They also said to clear the ipad and start over from scratch, and not restore from a prior device. (Such as my ipad 3rd gen). Tried this already on my first ipad air. I'm now on my 2nd one and I still have the issue.
They also said any problems of the actual device shutting down means I have a defective device. They said I should bring to apple store for replacement if it is randomly restarting on its own.