Since day one I've had this problem where my iPad suddenly goes to the white screen with black Apple logo. This happens no matter if I'm in an app or just on the home screen. Has anyone else had this happen to them?
It's an iOS 7 bug. It's called a crash or spontaneous reboot. I've had it happen multiple times on my phone, which was not jailbroken at the time. The fingerprint scanner caused it to happen frequently after I scanned my print. Deleting my stored prints and scanning them in again fixed that problem, but it did happen at other times as well. Update to 7.0.4 if you aren't there already. It may not completely resolve it, but it should help. Is your iPad jailbroken or stock?
You can tell the difference between a respring and a reboot because a respring doesn't require the passcode afterwards. Yours sounds like it's respringing. I've never had it happen on a stock device until 7.x (except when attempting to open Newsstand from within a folder on 5.x when a trick was used to get it in the folder).