WP 2.1 not closing mysql connection causing 500 errors

The connections in WordPress are opened with mysql_connect(), so they should not have to be closed as they are not persistent connections in the first place. They are closed automatically when the script ends.

If you really want to try using mysql_pconnect, just edit wp-includes/wp-db.php. It’s on line 52 towards the top. I cannot see how that would remedy your problem, however.

And this:

* If your PHP script does not close a connection once it is done using it, that connection will remain open for approximately 20 hours before the system resets it automatically.

is total nonsense. PHP’s own documentation says so:
From http://php.net/manual/en/function.mysql-close.php
Using mysql_close() isn’t usually necessary, as non-persistent open links are automatically closed at the end of the script’s execution.

Now, in theory, changing to mysql_pconnect would give a performance boost, if the database server didn’t totally break from attempting to handle a large number of persistent connections.

If you really want to force close connections, just change this:

function __destruct() {
return true;
}

to this:

function __destruct() {
mysql_close($this->dbh);
return true;
}

In wp-includes/wp-db.php.