You might be hosted on a service that does not use PHP as the Apapche module. When running as a CGI, the authentication methods used by podpress do not work (source: http://us3.php.net/features.http-auth).
Note: CGI is the default mode for Dreamhost, per their docs. There are instructions there on how to switch to the module, if you need to.
From what I've been able to see, podpress is looking for the HTTP_AUTHORIZATION header in the request headers for the premium feed. I found this odd, and am now wondering how old this code is. The docs list the proper $_SERVER variables as PHP_AUTH_USER and PHP_AUTH_PW. I cannot find another reference for the HTTP_AUTHORIZATION headers except for use in IIS:
Another limitation is if you're using the IIS module (ISAPI) and PHP 4, you may not use the PHP_AUTH_* variables but instead, the variable HTTP_AUTHORIZATION is available. For example, consider the following code: list($user, $pw) = explode(':', base64_decode(substr($_SERVER['HTTP_AUTHORIZATION'], 6)));
For reference, this is all happening in the podPress_validateLogin() function of podpress_premium_functions.php.
I'm going to keep digging into this, and would welcome any input people have.