Thanks matt. Note that if the page you need to authenticate is somewhere on your site other than under the WordPress root directory, you need to change the COOKIEPATH definition in wp-settings.php so that the auth cookie applies there as well.
I found that
define('COOKIEPATH', '/');
did the trick!
To further help others, note that the COOKIEPATH define is no longer in wp-includes/vars.php; it’s now moved to wp-settings.php in the WordPress root.
I found that
define('COOKIEPATH', '/');
did the trick!
