I have had an issue similar to this for quite a while. Was hoping that the 4.3 update would have fixed it but it still persists. For me the though, the issue happens on WIFI and not 3G/4G and only happens on certain places when I am on WIFI. Unfortunately my house is one of the places.
When the issue occurs, the only way to fix it is to reboot the phone. I haven't come across anything else that will work. I have seen mention of making sure the clock is right or removing your google account and I have even factory reset the phone a couple of times try and fix this problem.
This affects the play store, youtube, hangouts, and google+. Basically any app that uses Google services but does not affect the ability to access the Internet. It has to be something in Samsung ROM because at various times I have rooted and installed Cyanogenmod and the issue goes away. One I go back to a touchwiz ROM the issue returns. Since my town has finally gotten usable 3G and 4G its not that bad because I can just stay on 4G the whole time and minimize the issue.