我从来没有找到这个问题的真正原因。然而，这个“错误修复”确实为我解决了这个问题：

add_action( \'template_redirect\', \'handle_strange_bug\', 10 );

// "Fixes" the strange bug...
function handle_strange_bug() {
    global $post;

    $post_id = 123; // This is the post that makes problems.

    /* ===== Start of the bugfix.
     *
     * If the $post->ID is not set, but the URL indicates we are on the problem-
     * page then do a redirect to an alternative URL for the page. After the
     * redirect we always had a valid $post->ID, so 
     */
    if ( !isset($post->ID) ) {
        // The function is defined below.
        $my_url = get_current_url();

        if ( $my_url == get_permalink($post_id) )  {
            $good_url = site_url() . \'?page_id=\' . $post_id;
            wp_redirect($good_url);
        }
    }
    // ===== End of the bugfix.
}

// Helper function. Returns the full URL of the current request.
function get_current_url() {
    if ( @$_SERVER[\'HTTPS\'] == \'on\' ) { 
        $page_url = \'https://\'; 
    } else {
        $page_url = \'http://\';
    }
    $page_url .= @$_SERVER[\'SERVER_NAME\'];
    if ( @$_SERVER[\'SERVER_PORT\'] != \'80\' ) {
        $page_url .= \':\' . @$_SERVER[\'SERVER_PORT\'];
    }
    $page_url .= @$_SERVER[\'REQUEST_URI\'];
    // Remove the Query-string from the URL.
    if ( $pos_get = strpos($page_url, \'?\') ) { 
        $page_url = substr($page_url, 0, $pos_get);
    }
    return $page_url;
}