Dynamic connections probably wont help with this issue.
By default, Dreamweaver MySQL Connections (And Dynamic Coneections) use mysql_pconnect() to create the connection, this is a Persistant connection. On some servers that only allow a certain number of connections at a time, this can cause the issue you are running into. The fix for this is to use a non persistent connection by changing the mysql_pconnect() function call to mysql_connect()
change this line:
$dbConn = mysql_pconnect($hostname_dbConn, $username_dbConn, $password_dbConn) or trigger_error(mysql_error(),E_USER_ERROR);
to:
$dbConn = mysql_connect($hostname_dbConn, $username_dbConn, $password_dbConn) or trigger_error(mysql_error(),E_USER_ERROR);