The code

$sql = 'SELECT MAX(post_id)
FROM ' . POSTS_TABLE;
$result = $db->sql_query($sql);
$max_post_id = (int) $db->sql_fetchfield('max_post_id');
$db->sql_freeresult($result);

should be

$sql = 'SELECT MAX(post_id) as max_post_id
FROM ' . POSTS_TABLE;
$result = $db->sql_query($sql);
$max_post_id = (int) $db->sql_fetchfield('max_post_id');
$db->sql_freeresult($result);