Have you tried using different USB cables? As cables/connectors wear out, etc after so many plugs, bends, etc.
Check to make sure the pins/etc are clean in the microUSB port on the S3.
Maybe a pin got bent or something, so compare the ports to another microusb to see if anything is bent the wrong way.
Apart from that it is possible that the port on the S3 is busted.
Could also be an issue with the battery or the S3 is not registering the charge properly. Try the battery in another phone and try another working battery in the "broken" phone.