The Remote Server Returned an Error - (503) Server Unavailable (SharePoint Online)

Error Example:

Error while inserting new element: The remote server returned an error: (503) Server Unavailable.

Cause:

The same causes for the (429) throttling errors can lead to this, but error specifically is a hard block by the service due to exceeding usage limitations. You may have been syncing too many connections at the same time, or repeatedly starting a very large sy​nc over and over in a short period of time. See How to: Avoid getting throttled or blocked in SharePoint Online for more information.

Resolution/Workaround:

As the same conditions can lead to this state, see the article (429) Errors / SharePoint Online Throttling for further troubleshooting steps. You may need to stop using the Cloud Connector for a while to allow the usage amount for the time period cool off so they won't be throttled/blocked on a retry.

​