Maybe you should both RTFM a bit more.
mysql_pconnect() acts very much like mysql_connect() with two major differences.
First, when connecting, the function would first try to find a (persistent) link that's already open with the same host, username and password. If one is found, an identifier for it will be returned instead of opening a new connection.
Second, the connection to the SQL server will not be closed when the execution of the script ends. Instead, the link will remain open for future use (mysql_close() will not close links established by mysql_pconnect()).
Which tells you that you CAN'T close pconnect (avoid pconnect, it's more of an accident looking for a place to happen than a solution in search of a problem.)
While PHP can run with transparent session IDs auto-appended onto URLS, it has had some reports of unreliability in the past, mostly associated with the URL encoded session ID disappearing.