When you say the logs do not yield any insight, was that information provided through a case with Tableau Technical Support? Tableau's Server logs can be a tricky thing use to diagnose issues. In the Engineering Team, we regular weekly meetings where we discuss cases and review logs as a group to better diagnose and trace issues back to their root cause. Many times we'll identify what appears to be an insignificant event in the logs can provide insight into the root cause. If you haven't already, I would suggest opening a case with Tableau Technical Support and provide the symptoms, exact date and time of error, a copy of the server ziplogs (encompassing the date of the incident) along with the name of the workbooks or data sources having issues and screenshots of any error messages received by the user.
Thanks and hope that helps!