iPhone 5 and 5s lock screen flashing Apple logo We have three iPhones in my house: two 5's and one 5s. Over the past 6 months every few weeks they glitch. What happens is that at exactly midnight eastern time all three phones start showing the lock screen for two seconds, followed by a second of a black screen, followed by five seconds of the Apple logo on a white background. During this time the phone is running. When on the lock screen you can actually swipe left and start entering your unlock code, but you will get interrupted. This usually goes on for at least 6 hours. Hard resetting the phone does not fix it: you just boot to the same state. Restoring from a backup does fix it and seems to be the recommended solution on the Apple forums.

If I do not do a restore from backup, the problem resolves itself usually by around 10am.

This happened with all iOS 7 updates including the 7.0.4. 

This is a huge problem. First, it lights up the whole room and drains the battery. If not on the charger, the phone will die and our alarms will not go off. If on the charger, the phone will keep buzzing like you just plugged it in. BTW, we use standard Apple cables and chargers. Restoring from backup takes a long time and I do not wish to do that for three phones in the middle of the night. There are of course other inconveniences, like not being able to dial 911.

Someone please tell me I am not alone in having this issue. It seems like a huge bug in iOS and in just a bit I am going to try to call Apple to see if I can figure out how to report it. In the meantime, I'd just like to see if the three iPhones in my house are the only ones that are experiencing this or if this is widespread.

Edit: Turns out an iPad Air we have also had the same problem. The only iOS device that did not is a third generation iPad.

Edit 2: Just called Apple. Their senior support person has never heard of this issue, so they are escalating to the development team. We'll see what they say...

Edit 3: Have not experienced the same issue but never heard back from Apple. Seems like the 7.1 update helped. If anyone else is still experiencing this issue, please respond.
I had this exact same problem. It has to do with recurring calendar events. This mainly occurs when the phone is syncing with Microsoft Exchange, but may occur in other circumstances. You need to find any recurring calendar events and simply delete them. Adding an end date will not fix the problem. It took me about a month of looking through device logs to figure this out.