Persistence problem, I think

Persistance won't work for what you are trying to accomplish.

For one, in the recordset you are not using the persistence variable.

For 2, your select list is a multiple select list, this passes the selections as an array, you need to add code to convert the array.

for 3, your recordset is using equals:
SELECT * FROM member_list WHERE member_id = <select value>

since you are using a multiple select list, you would need to convert the army of numbers to a comma separated list and use IN() in the recordset.

so to save the selections made to a session, you will need to add nhand coding:

<?php
if(isset($_POST['member_entity'])) {
$_SESSION['member_entity'] = implode(", ", $_POST['member_entity']);
}
?>

then you will need to hand edit the recordset query code:
$query_rsRollCallVerify = sprintf("SELECT * FROM member_list WHERE member_id = %s", GetSQLValueString($colname_rsRollCallVerify, "int"));

to:
$query_rsRollCallVerify = sprintf("SELECT * FROM member_list WHERE member_id IN(".isset($_SESSION['member_entity'])?$_SESSION['member_entity']:"0".")");