The HyperText Transfer Protocol (HTTP) 406 Not Acceptable client error response code indicates that the server cannot produce a response matching the list of acceptable values defined in the request's proactive content negotiation headers, and that the server is unwilling to supply a default representation.
In layman's terms: I think your server has an access rule defined that is preventing Dreamweaver from browsing the site directly. It might be a ModSecurity setting that only allows browsers to access web pages (not Dreamweaver) as a security measure.
Who hosts the site? They may be able to access the ModSecurity log file to see the issue and enable dreamweaver to access the necessary database files. Dreamweaver tries to post to a hidden file in the _mmServerScripts directory. This error means that your server is rejecting the post and refusing to return the necessary data.
I tried to disable mod_security by adding a .htaccess file to the _mmServerScripts folder, but that didn't seem to work. I think your hosting company may be able to shed some light on it by looking at the server logs when accessing that folder.