Ok, best chance might be the S3 forum, as this is probably either hardware or system software. I'll move the thread over there.
The only software fixes I can think of are a factory reset (wipes all apps and data, so back up anything important first) or re-flashing the phone's firmware (which will also wipe the phone). No guarantee either would work. But the best would be to see whether the S3 experts have any other ideas first.