The URL for "Analyze Board" is something like
http://www.redhotpawn/core/playchess.php?gameid=1234567#
If I still have the Analyze Board window open from the previous move, my browser [IE6] just switches me to the out-of-date board.
Suggestion: The URL should include something like "&move=29" so that browsers know that the previous window cannot be re-used.