You can run them as soon as you are done with them. PHP *should* release the resource at the script termination (should being the keyword) if you don't issue a shutdown. The purpose is to free up memory that you no longer require to be held, so if you use large datasets, free them as soon as you can.
MySQLi with prepared statements are different. You should close the statement as soon as you are finished with them; depending on the usage they can block other commands until they are free. Since you need to move to MySQLi or PDO soon anyways, you may as well get used to issuing free now.
As of PHP 5.5, the MySQL library has been officially deprecated. It is recommended to move to either MySQLi or PDO libraries for your mysql connectivity. See here for help choosing which interface you prefer: http://php.net/manual/en/mysqlinfo.api.choosing.php