90% of the time charging issues are caused by dirty pin connectors on the s3 port they get filled with crap and every time the charger is plugged in it compacts this dirt and makes things worse i have fixed all my friends s3's and all of them had the same problem
fix: 1 can of contact cleaner
spray a small amount inside phone port and then in charger plug insert and remove plug about 6 times respray both the plug and charger port and repeat this about 5 times and all is good if its not your phone port must be damaged and will need repairing by a technician.
i have had no problems doing this but still attempt at your own risk as i will not be held responsible for any broken phones