iPhone 5 date and time issues! iOS 7

So here's the problem - about a month ago, my iPhone 5 (with iOS 7) started randomly changing the date and time. The only thing that works is to turn it off and turn the phone back on again - each time I do this, FaceTime and iMessage shut off.

1) I went to the Apple Store and they told me it was a Verizon issue.

2) I went to Verizon, and they sent me a new (refurbished) phone....still happened.

3) I reset the settings....still happened.

4) I went back to the Apple Store and they said that it was because there was a "bug" in my iCloud. Restored to factory settings and set it up as a new phone (without taking anything off of my cloud) - still happened.

5) Turned off the automatic date and time setting - still happened.

6) Went back to the Apple Store and was told it is an issue with IOS 7 and there's nothing that can be done until there's a new update.

What?!?! Help!