DO NOT use pconnections. lol. In phps' mysqli this was drop because of the number of problems it caused. If you can code ask them to send you the error log for your domain and look through it, find the script/s and make sure the database connection closes. Maybe even upgrade the sql calls the mysqli as you can clean up resources faster
$mysqli = new mysqli("db_host","db_user","db_psswd","db");
$result = $mysqli->query(select your query here);
WHILE($row = $result->fetch_assoc()){
//work done with data sets here
}
$result->close();
$mysqli->close();
To some this might look odd, this is object oreiented php using mysqli. But the main thing to notice is the 2 objects I closed.
$result->close();
This cleans up all resources used to make the query. Ram, CPU time, all cleaned up
$mysqli->close();
Closes the database connection object.
If you can't code... Get a less anal host. Interserver.net has done me very good.