WP Login forms action URLs displayed as pretty URLs in browser (ex with Restore Password)

Step 2. However, when I submit an un-matching password, the form is redisplayed and URL is now http://example.com/wp-login.php?action=resetpass&key=xyz&login=zyx. Notice, that action has changed.

When I attempt this with an invalid key I get redirected to http://example.com/wp-login.php?action=lostpassword&error=invalidkey.

Anyway, the infinite loop is occurring because you are the condition in_array( $action, array('rp', 'resetpass') ) remains true for the url you are redirecting to, so you end up in a redirect loop.

The solution is to check that the requested url differs from the redirect url:

function pretty_login_urls_form_action_fix(){

    $action = isset( $_REQUEST['action'] ) ? $_REQUEST['action'] : '';
    if( in_array( $action, array('rp', 'resetpass') ) ){

        $requested_url  = is_ssl() ? 'https://' : 'http://';
        $requested_url .= $_SERVER['HTTP_HOST'];
        $requested_url .= $_SERVER['REQUEST_URI'];

        $redirect_url = home_url( '/password-restore?action='. $action .'&key=' . urlencode( $_GET['key'] ) . '&login=' . urlencode( $_GET['login'] ), 'login_post' );

        if( $redirect_url !== $requested_url ){         
            wp_redirect( $redirect_url );
            exit;
        }
    }
}