here's the fix. simple terms, after doing a factory wipe I tried this and it works! just sucks we have to do this still on android 4.0.4...
4.scroll down to internet
5. clear data!!!!
6.I would reboot the phone... this will reboot and wipe all bookmarks and favorites. save them before doing this...
from MY SIII in sunny FL.
This problem happened to me as well. For the longest time I didnt know why but then I shut my sync off and realized it stopped. After further investigation it seemed that my google account that i set up when I first got my phone was the problem. All I did was delete the account and then re-add the account. here are the steps I took to determine which account it was as how to delete it.
go to settings > accounts and sync (down at the bottom in the personal section) > click each account 1 by 1 > click sync now. usually the account with the problem will give you the error message every time you try to sync. Delete this account and then re-add the account and this should take care of your problem.