Changing odbc_connect to odbc_pconnect causes the script to fail, complaining that the $odbchandle "Supplied resource is not a valid ODBC-Link resource" on a odbc_close($odbchandle).  Leaving the code as is works perfectly.

...
    // Connect to the database
    $odbchandle = odbc_connect( $DSN, $USERNAME, $PASSWORD );

    if ( $odbchandle ) {

      // Query for the user record
      $query = "SELECT * FROM Subscribers WHERE SubscriptionID='" . $subscriberID . "'";

      $queryresult = odbc_do( $odbchandle, $query );

      // ...
      odbc_close( $odbchandle );
...

It _seems_ that commenting out the odbc_close() when using the odbc_pconnect() causes the warning to go away.  Naturally this begs the question about when persistent handles go away... but still, I wouldn't think odbc_close() causes a warning.  Using odbc_close_all() works just fine, with no warning.