I just got 2 iPhone 5's and it appears to have a problem with randomly changing the the date and time. I have experienced this on both handsets and it is bit frustrating. This appears to be a Verizon iPhone 5 issue only as describe by other Verizon clients on the apple discussion boards. https://discussions.apple.com/thread/4347494?tstart=0
this afternoon I had just received a SMS message and then noticed the time and date hat reverted back to sometime on september 2. to fix it I turn on airplane mode and wait about 30 seconds turn it back on it thn fixes the time once it gets a read from the tower.
If others are having this problem please chime in or if you have discovered a solution that works please let us know.