mysql_pconnect() will keep opening new connections using constant strings.
I see this through "mysqladmin processlist".
I'm using MySQL 3.21.29-gamma-log.
Compiled as Apache 1.3b5 module with 'configure --with-my-sql --with-apache=/x'

Script like:

$sql_link = mysql_pconnect("localhost","user","password);
if ($sql_link < 0):
	exit;
	endif;
$query = "select count(*) from sample";
$result = mysql_db_query("test",$query,$sql_link);
$num = mysql_numrows($result);
$i = 0;
while($i<$num):
	echo mysql_result($result,$i,"field");
	$i++;
	endwhile;
mysql_close($sql_link);

In theory the mysql_close() wouldn't matter, but i have the same
problem whether i leave it or not.