There may be several variations of this issue but I believe it mostly occurs because the internal clock on some S3's simply do not keep time well. If the time updates regularly then the problem is hardly noticeable. However if the interval between time updates is longer than the internal clock error you will notice a time variation until the next update occurs. This could be just a few minutes per day or if your internal clock is really having problems, even more. In normal use I do not believe the time updates by itself more than once a day, if that. And since there are so many phones out there now I further believe the factory software setting for the time correction interval is getting longer with every OS update to cut back on overall user bandwidth which is why more people are now noticing time fluctuations on their phones.
So what to do? You can force a time update by resetting the phone everyday or by turning Airplane mode on and then off. This provides a temporary fix but if a smart phone tells time so poorly that it has to be reset each day that's hardly a fix. Imagine having to reset your watch everyday. If your S3 is still under warranty insist that it be fixed or replaced as I believe the core issue is a hardware malfunction with the time circuitry. If it's not under warranty then the only free fix would be to find a way to have the phone update the time more frequently by itself. I don't believe there is a way to do this via any user settings. Instead you would need to download a clock synchronizing app such as ClockSync. This would resolve the problem but unfortunately in order for the app to automatically get access to the time setting you'll need to root the phone. This is not rocket science but it's not that easy either and many people can't or won't root their phone for a variety of reasons.
It's possible Android or your carrier might someday provide a fix by allowing the interval between time settings to be adjustable but I wouldn't hold my breath waiting for this fix because I don't believe the problem is widespread enough for them to bother, and then there's the bandwidth issue. I really hope I'm wrong about that because so much relies on having an accurate clock, from meetings to alarms to messages, and a smart phone that can't tell time is not so smart.
If you want this problem to be addressed you'll need to make some noise about it. Best of luck.