Yes. I know what you are all talking about. First off I love my new iPhone. It's the first I've owned even though I been a long time Mac and iPod user. My first iPhone arrived scratched from the factory which is a whole other issue. They got a extra $100 from me because Verizon only had the 64gb in stock and I didn't want to wait another couple if weeks.
Anyways, back to the time issue. I just started having it yesterday. Only the time was affected by 4 hrs. I set to manual and when I awoke this am iMessage said that my times settings needed to be updated. I did and everything was back to auto working fine. Then at lunch I lost 30mins and 4 days behind. Switched back to manual which iMessage came up again to remind me to update. Finally, I called Apple. They told me to do everything short of resetting my phone. When I tried auto again it worked (I was on wi-fi). Apple said if you put on Manual and time doesn't change then its not a software issue. He didn't come out and say it, but basically he said that Verizon was the problem. Then later this evening after being on auto for an 1hr when I left wi-fi range and switched to LTE the time issue happened again. I finally went back to manual. I noticed that when you switch between auto and manual when in LTE Range, the time doesn't display properly and gets even further off. It had me back on Sept 15.
THIS SEEMS TO BE (from my experience and opinion) A VERIZON LTE PROBLEM!!
I didn't have any issues with my Droid X losing time on the 3G network. Verizon will not admit its there problem and Apple want admit its theirs. Best thing is to set to manual and deal with it. Of coarse that ***** when traveling, but its the only way I can be assured my alarms and calendar appts. will be right. Until Verizon works out the bugs off LTE this will probably always be a problem. I mean, if you have turn off 4G LTE to keep your time synced up, I could have just saved $300 and got a 4S. That's one of the main reasons I went to the i5.