Alrighty, I am going to the Apple Store AGAIN tomorrow to see about getting this ****** phone fixed.
And I can prove (at least for my iPhone) it has nothing to do with background refresh OR battery life.
Background refresh has been off. Always has been. My battery has ranged from 25% to 100%, both plugged into a power source and running on the battery.
This piece of **** has rebooted itself 100+ times since Monday. Monday alone, I had it reboot something like 30 times in the span of 45 minutes. The reboots range from a 2 second Apple logo to a full restart which takes much, much longer. Every morning when I wake up, my phone has apparently frozen mid reboot as the screen is black and the phone won't respond until I do a hard reset. Occasionally when I get a reboot, the top or bottom half of the screen will turn blue, green, or red. The phone occasionally locks up and won't respond to anything for 5+ seconds then it carries on like nothing happened. There is literally no rhyme or reason to these reboots. It will happen when it is just sitting next to me doing nothing, when I am checking email, when I am browsing the internet, when I am staring at the home screen, when I am in settings, when I am running apps, when I am playing games. It doesn't matter what the battery level is, it doesn't matter if it is plugged in or not. It is unaffected by WiFi connectivity. It has nothing to do with my data on this phone was set up like new and not restored from iCloud.
I am sick and tired of this. I won't be leaving the Apple Store tomorrow until I can get a promise that this **** will stop when I walk out of there.
Oh, and iOS 7.0.3 didn't do anything to help this.