This method is a GUARANTEED fix for the 'online login is currently unavailable' or 'you need to be online in order to sign' while your internet connection is just fine. I've seen that this method has worked for everyone else who didn't manage to sign into origin after they put their time on automatic.
So:
1 Uninstall origin completely. Don't uninstall your games, just Origin.
2 Go to this link: https://filehippo.com/download_origin/ .. It should be Origin version 10.5.41.272633.
3. Download the Origin from this link and while in the pre-install menu, it is VERY IMPORTANT that you UNCHECK the box saying 'Keep origin and my games up to date'.
4. Click install and Sign in and play !
Do not exit origin or you will have to repeat. Good luck
