Warning: mysql_affected_rows() [function.mysql-affected-rows]: A link to the server could not be established in /home/path_to_my_blog/wp-includes/wp-db.php on line 183
But, the publish/update action if actually executed ! So I tried to get in the code and just replacing this line
$this->rows_affected = mysql_affected_rows();
by this one
$this->rows_affected = mysql_affected_rows($this->dbh);
solved the problem.
Is it so difficult for the Wordpress Team to put explicitly connection link to the database server ?