IPhone 5 displaying the wrong time. (AT&T)?

I have an iPhone 5 from AT&T and a couple of days ago it started displaying the wrong time. I can set my time/date settings to automatic/manual and it still displays the incorrect time. I'm able to fix the problem temporarily by turning Airplane mode on and off, but after a few minutes the time will display incorrectly. It will either be a few minutes/hours ahead or behind. Downloading another clock app doesn't help because it's still dependent on the system time so the time for third party apps are incorrect as well.

These are some of the things I've tried so far:

- Respring
- Factory Reset from the phone
- Factory Reset from my Mac Book
- Replacing SIM Card

These the time discrepancy temporarily but eventually the time will be wrong.

I'm out of ideas and my phone is no longer under warranty so I would have to pay close to $300 to get a replacement… Money that I don't have.

I've heard that it could be battery related. Would replacing the battery help?

I'm open to any suggestions that anyone might have.

Get a GPS app. That will display the correct GPS time regardless. I think inside the phone is a RTCC (Real Time Clock Calendar) which keeps time when you aren't connected to your data plan. The internet has many internet time servers, but if you your data is not on, the RTCC is supposed to provide accurate timekeeping. There may be a problem with that circuit, you might take it in to the Apple store and have it looked at.

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