iPad Air Spontaneous Reboots?

While I love my new iPad Air, I've had a number of spontaneous reboots over the past month, and wondered whether anyone else was experiencing anything like this. Tonight's most recent incident occurred less than six hours after performing a reset to factory defaults, then a restore from an iPad 3 backup, and happened when I clicked on a link in a spam email. The link opened Safari, I saw it was spam, and immediately went back to Mail to delete it, which caused an immediate spontaneous reboot that only took 10-15 seconds to return me to the login screen.

I've had a couple of these situations over the past month, and had assumed some pre-iOS 7 app was burping, which would eventually resolve itself with app upgrades. However, now I'm not so sure. The situation slowly worsened until this morning, when it blew up. Last night I played around with a new iOS 7 version of Flightradar24. This is a cool app that tracks hundreds of flights world-wide dynamically updating a global 3D map with their movements and info from their flight transponders. So, you can follow individual planes in flight, with their call sign, altitude, speed displayed from takeoff to landing. Anyway, I followed a few flights for a couple of hours with the app, quit and went to bed, leaving Big Clock2 running on the screen overnight. This morning, I quit the clock, and started up the Podcasts app to listen to a show during my workout, but Springboard's behavior seemed a bit odd, so I did a simple Restart to clear the RAM with the power button. That didn't help, so I then tried a hard reset (power + home button) to also clear the caches, which also didn't help. In fact, things got worse because I then couldn't even log in at the login screen because the swipe-to-login feature didn't work. Another hard reset finally allowed me to login, but then Springboard was missing a bunch of folders holding over a hundred installed apps. Settings showed the apps were still there, but they weren't being displayed. It didn't occur to me to try the Settings/General/Reset All Settings option to potentially force Springboard to rebuild its display preferences for installed apps, so I proceeded with the full iTunes Reset to Factory Settings option instead, and spent the rest of the day tweaking everything to my preferences.

Since this isn't a pristine rebuild, but rather a reset to factory settings + restore from backup option, I can't really tell whether I simply have some corrupted setting from my backup doing bad things, or an iOS 7 software or iPad Air hardware issue. So, I'm turning to the cohort of new iPad Air users for info.

So, have any of you new iPad Air users been experiencing occasional spontaneous reboots while using your iPad? These are quick reboots, taking only a fraction of the time common with a full startup from shutdown or from a hard set reboot process. It's too soon to query the Apple folks, since I can't force the behavior to show them. But, it is worrying. I don't really know whether I have a software or hardware issue yet. I'm guessing software, but even in that case I don't know whether it's app related or iOS 7 related.