The http authentication is defined in the .htaccess file in your website's root directory and/or in subfolders, if you have folder specific control files.
In this .htaccess file, you can set a password protection to your site or some directory, like
AuthName "Member's Area Name"
AuthUserFile /path/to/password/file/.htpasswd
AuthType Basic
require valid-user
In my earlier example, the site my.domain.com was password protected and this is why the plugin could not sent the lead information:
http://my.domain.com/crm/index.php?entryPoint=WebToLeadCapture
Edit or remove the (hidden) .htaccess file, and the plugin should work. As far as I can tell, there is nothing wrong in the actual plugin. It just cannot penetrate the password protection.