This error can occur if you don't have permissions to the directory specified as the thumbnail directory.
You can check your log files to see the error. The log.txt file located in %localappdata%\Avail\AvailRevitPlugin\[YEAR], where [YEAR] is the version of Revit you were running when you experienced the error. For example, since you experienced the error on the Nov. 2nd, there will be a log file titled log.txt.2018-11-02 in this directory.
When the Project Thumbnail Generator in the AVAIL Browser for Revit starts the thumbnail generation process on the specified project, it first tries to access the path \\srvnas01\Library\AVAIL\Thumbnail_DO_NOT_TOUCH\. This generation process then attempts to create the required sub-directories needed to store the thumbnail files of the selected project. Unfortunately, the log is showing that access is denied to this path. In order to fix the issue, you will need to update the security permissions on the \\srvnas01\Library\AVAIL\Thumbnail_DO_NOT_TOUCH\ directory so that you (or a group you are a member of) has at least Modify permissions.