Updated to iOS 7.1, but constantly reboots

I have an iPad mini, which I bought sometime last year, and I haven't experienced any issues until the iOS 7 update. After that, it would constantly reboot and give me the "black screen of death" several times a day. While some users said that they experienced it more often after their battery dropped to 30%, I noticed no difference. The bug was reportedly supposed to be fixed with iOS 7.1, but after I updated it, the reboots only seemed to intensify.

Now, I can't use my iPad for more than a few minutes before the screen turns black and it reboots itself. It often repeatedly reboots and I don't even see the **** lock screen until it has rebooted itself at least 5 times in a row. I've tried restoring it, and I think my warranty is over. This is just so frustrating because it's basically useless. Is there any way to fix this, or will there be an update? Because 7.1 didn't seem to do anything for me.