when you enable such feature, Admin Tools creates a file that will be parsed by your webserver Apache. After reading it, your webserver will ask an additional username and password to every visitor, way before WordPress or our software has a chance to run. This is why it's very efficient: it will block requests even before you start serving them.
That being said, sometimes some webservers doesn't have this feature enabled, resulting in 404 error because they can't serve the "request username and password" page correctly.
In this cases there's nothing we (you and us) can do: you should contact your hosting provider and tell them that you want to add Basic Authentication using Apache on your site. They should know how to fix this issue.
Developer and Support Staff