Version 2.2.xx and above of Cloud Drive Mapper requires the end user to have edit or read permissions on the parent SharePoint site that is being mapped to. 

For example, if the mapping was to

Then the permissions would need to be applied on 'examplesite'.

However, it's possible to achieve using read permissions too, providing that the setting below has been applied. This is a per tenancy setting and will apply to any read permission set on any site. 

Under > Site Permissions   >  Permission Levels > modify the permissions on read  -  Ensure that enumerate files and folders in a Web site using SharePoint Designer and Web DAV interfaces is ticked 

If the above hasn't resolved the issue then the user can be added to the site visitors group under the permissions on the site and then retested.

If you have any questions about Cloud Drive Mapper and how it uses SharePoint permissions please contact