I haven't posted in this thread in a while. I've been having the issue since day 1 with the three iPhone 5's I purchased for my family. We're all still experiencing the time/date problems here in western North Carolina (Cherokee, NC).
I've tried all the resets possible - reset settings, reset network settings, reset phone (erasing the device). I've set the phone back up from an iCloud backup, from iTunes on my mac, started it as a new device with no backup. Nothing has helped - even temporarily. Time shifts occur every day.
I've toggled all the settings possible - set auto time date off/on, time zone support off/on, locations settings off/on, etc. None of those worked.
When the time shift occurs, toggling the phone to Airplane mode and waiting about 10 seconds for the phone to display Searching where the Verizon logo usually appears and then toggling it back off works. That's easier on the phone, I believe than all the resetting.
The ONLY temporary fix I've discovered is to go to Settings>General>Cellular>LTE and toggle LTE off. If I turn LTE off at my house, then my time stays correct. I can use LTE at my work (37 miles away) and the phone never changes the time. However, disabling LTE disables the reason to even have the 5. It's very disappointing to have been dealing with this issue since launch day and still no fix.
Even more frustrating is the bizarre sluggishness with which blogs, tech newsies and podcasters have picked this up. Some still even haven't reported on it. I reported the issue to Today in iOS podcast and Rob did do a story on it, but he seemed to be poking fun at me and all of us who are having this issue. He made it seem like we were making much ado about nothing. Perhaps I didn't interpret him correctly, but that's how it came off sounding to me. Check out his latest podcast from last week and see what you think . I didn't want to email him back on that because I was kind of disappointed that he didn't seem to take the issue seriously. For those of us that this issue is happening to, I can assure anyone that we take it very seriously.