I am posting this because I hate this issue so much and there really is little support on fixing it. I do not know what causes the issue, nor do I know a once-fixed, always-fixed. I will say this though: --To anyone having this issue, I have found that there is always an app that is messing the sign-in up. NOT always a downloaded one, either. I do not think the error is always 2-step verification, as I don't have that but still get the error. I recommend that you go to Accounts & Sync, and see which parts of your Google account are failing. Then search under ALL apps in Manage Applications for anything that may be related to what fails. On my last hunt, my contacts would not sync and cause the error. I ended up force closing the System app called "CSPeopleSyncService" and then typing in the Authentication characters that it asked for. It fixed it. It was the 5th app I force closed. I hope this helps anyone who is trying to resolve their issue. I have read that factory resets do not always fix the issue, so only do that when the other option is smashing the phone. Just think outside the box, cause there are SO MANY APPS that connect, in some way, to some part of your Google Account. Any of these apps will be possible causes. Happy hunting!