Why would admin-ajax.php redirect to the home page for logged out users?

It only redirects when accessed directly, as do all files located in wp-admin/. AJAX requests should work fine regardless of authentication status.

Edit: wp-admin/admin-ajax.php should not redirect in any situation. Perhaps a plugin is redirecting all unauthenticated users to the homepage? By default, accessing files inside wp-admin/ when not logged in should redirect to the login page.