One possibility to consider, it could be that the phone service providers network signal is not strong enough in your area. You can check this by looking at status of the icons at the top of the phone.
Not sure which icon it is as I don't have access to a Galaxy S3, but there is some info here and also in the manual that you should have received with the phone:
http://www.androidentity.com/guide-to-samsung-galaxy-s3-notification-bar-status-bar-icons
Is the Phone on contract or is it Pay-as-you-go?
If the answer is yes to both of these and the current phone service network signal strength is the problem, you could try using a different phone service providers Sim that has a stronger signal where you are.