Hard to say what is going on, and I agree you should take it to the Apple Store, barring a miracle fix between now and then. I'm just throwing out ideas because, well, that's the way I am. So here I go again, and sorry if it's already been asked and I missed it. Have you cleared out the cookies and data lately?
No problem asking. Yes, I have cleared cookies, history, turned it off completely. I think it is the iPad Air itself, or the way this one in particular is behaving.
Since not everyone with the Air is having these issues, I think, like most manufactured goods, even though they are mass produced, and most likely with a lot of robotics, there still could be issues with some, but not most. The same goes with cars, microwaves, anything manufactured. Some companies will do a mass recall and some are ordered to. Something in my iPad Air and other people's iPad Air does not react as designed and expected to the iOS. If that is the case, I doubt all the updates in the world will fix them. The Apple assembly plant where this was put together may have received some faulty parts and there were so few, it wasn't discovered. There were a LOT of these sold.
We had a Samsung TV that died fairly early, less than a couple months. My husband, who is a licensed professional engineer had to check it out. He knew what the issue was and looked at something, schematics(?) and found out where on that huge circuit board that would be handled. He looked and looked for a few days. He used his little probe thingies. He finally added a magnifying glass to his arsenal. He found a soldering joint that had a very minuscule break in it. He removed the soldering job done by, most likely a robot, and redid it himself and cleaned up others while he was at it. The TV is still working today. This was a few years ago. So, my point is, even robots can do a messy job sometimes. So, there may be pads out there that have a rare glitch in the manufacturing, soldering, assembly, or glitchy parts. Most pads will be fine, but the few of us who have the ones done with the glitch, have issues.
I am not saying this is the case, just a theory. I am not a techy person, but I will get it replaced in a few weeks and see what happens.