If your emails or calendar events have suddenly stopped syncing, you most likely need to update your Google or Office 365 password in Nutshell.
Follow these steps to reconnect your email sync from scratch, which helps solve most sync issues:
Go to this page and revoke access to your Gmail or Office 365 account by clicking "Disable", then "Forget this account and add a new one", then "Disconnect".
Re-enable access and follow the steps in the wizard to get reconnected.
Once you've done this, you should be able to click "ignore" on any visible errors to clear them.