Well, it sounds like you have the RSS feed 'protected' and requiring a log-in.
The problem is that the user will have to log-in and set a session with the site to get the authentication to look at the RSS. Obviously an RSS reader can't do that. So, really, you can't password protect it. What you could do is add a requirement for a random hash to be on the end of the RSS feed (http://example.com/protected/rss?hash=whatever) and then assign that hash to a user and then there is *some* sort of authentication there.
Otherwise you could look at implementing basic http authentication: http://user:firstname.lastname@example.org/protected/rss - http://php.net/manual/en/features.http-auth.php