As I understand it "mysql_pconnect" is used for persistent connections only which I don't use.
In fact it has been suggested even though offered in UBB setup not to use it.
Control Panel » DB, Paths & URLs
Use Persistent Connections?
If that is enabled I would turn it off.
If you can't open the control panel, you could edit the includes/config.inc.php file.
To disable it, it would be like:
'PERSISTENT_DB_CONNECTION' => ' ',