That's a long title, but the problem I'm solving here is very specific. My 6-year old daughter likes trying to guess the restrictions passcode I've set on her iPad. (She's a pretty good spy, too—she managed to get a couple of digits by watching in the reflection in my glasses while I was typing it in once.) I was just about to let her buy a single from iTunes Store, when I realised she had been guessing again, and the device had been hit with a lockout period of over 17,000 minutes. (I'm not sure how many times she had failed in total, but that seems extreme!)
The solution is simple, and doesn't involve reseting the device or restoring from a backup. Just go to the date and time preferences, and roll the calendar year over by one. Go back to the restrictions keypad—the lockout will have expired, and you can enter the passcode. Return to date and time preferences and roll the year back. Done.