Since when does session_destroy() kill any type of connection? According to PHP Manual - session_set_save_handler(), by default all it does is delete a file from disk.
In any case, once you call mysql_pconnect, you're basically telling PHP not to allow that script to close the connection to the database. Kinda like getting a phone call where more than one person wants to talk to you so they just hand their phone on to the next person. No need for each person to hang up and dial your number if they are all at the same phone at relatively the same time.
Perl / MySQL / HTML+CSS