I was hoping just a small change to /includes/functions/sessions.php would do the trick.

For example, I tried changing the line $SESS_LIFE = 1440 to $SESS_LIFE = 14409 yet the cart still was gone after 24 minutes.

Here's the sessions.php code from Zen Cart version 155a if anyone wants to take a quick look and make a suggestion . . .

Code:
<?php
/**
 * functions/sessions.php
 * Session functions
 *
 * @package functions
 * @copyright Copyright 2003-2016 Zen Cart Development Team
 * @copyright Portions Copyright 2003 osCommerce
 * @license http://www.zen-cart.com/license/2_0.txt GNU Public License V2.0
 * @version $Id: Author: ksteslicki  Sun Jan 25 17:45:51 2015 -0800 Modified in v1.5.5 $
 */
if (!defined('IS_ADMIN_FLAG')) {
  die('Illegal Access');
}
  if (IS_ADMIN_FLAG === true) {
    if (PADSS_ADMIN_SESSION_TIMEOUT_ENFORCED != 0 && SESSION_TIMEOUT_ADMIN > 900) {
      $SESS_LIFE = 900;
    } else {
      $SESS_LIFE = (int)SESSION_TIMEOUT_ADMIN;
    }
  } else {
    if (defined('SESSION_TIMEOUT_CATALOG') && (int)SESSION_TIMEOUT_CATALOG > 120) {
      $SESS_LIFE = (int)SESSION_TIMEOUT_CATALOG;
    } else
    if (!$SESS_LIFE = get_cfg_var('session.gc_maxlifetime')) {
      $SESS_LIFE = 1440;
    }
  }

  function _sess_open($save_path, $session_name) {
    return true;
  }

  function _sess_close() {
    return true;
  }

  function _sess_read($key) {
    global $db;
    $qid = "select value
            from " . TABLE_SESSIONS . "
            where sesskey = '" . zen_db_input($key) . "'
            and expiry > '" . time() . "'";

    $value = $db->Execute($qid);

    if (isset($value->fields['value']) && $value->fields['value']) {
      $value->fields['value'] = base64_decode($value->fields['value']);
      return $value->fields['value'];
    }

    return ("");
  }

  function _sess_write($key, $val) {
    global $db;
    if (!is_object($db)) return;
    $val = base64_encode($val);

    global $SESS_LIFE;
    $expiry = time() + $SESS_LIFE;

    $sql = "insert into " . TABLE_SESSIONS . " (sesskey, expiry, `value`)
            values (:zkey, :zexpiry, :zvalue)
            ON DUPLICATE KEY UPDATE `value`=:zvalue, expiry=:zexpiry";
    $sql = $db->bindVars($sql, ':zkey', $key, 'string');
    $sql = $db->bindVars($sql, ':zexpiry', $expiry, 'integer');
    $sql = $db->bindVars($sql, ':zvalue', $val, 'string');
    $result = $db->Execute($sql);

    return (!empty($result) && !empty($result->resource));
  }

  function _sess_destroy($key) {
    global $db;
    $sql = "delete from " . TABLE_SESSIONS . " where sesskey = '" . zen_db_input($key) . "'";
    $db->Execute($sql);
    return TRUE;
  }

  function _sess_gc($maxlifetime) {
    global $db;
    $sql = "delete from " . TABLE_SESSIONS . " where expiry < " . time();
    $db->Execute($sql);
    return true;
  }


  // Initialize session save-handler
  session_set_save_handler('_sess_open', '_sess_close', '_sess_read', '_sess_write', '_sess_destroy', '_sess_gc');
  // write and close session at the end of scripts, and before objects are destroyed
  register_shutdown_function('session_write_close');


  function zen_session_start() {
    @ini_set('session.gc_probability', 1);
    @ini_set('session.gc_divisor', 2);
    if (IS_ADMIN_FLAG === true) {
      @ini_set('session.gc_maxlifetime', (SESSION_TIMEOUT_ADMIN > 900 ? 900 : SESSION_TIMEOUT_ADMIN));
    } elseif (defined('SESSION_TIMEOUT_CATALOG') && (int)SESSION_TIMEOUT_CATALOG > 120) {
      @ini_set('session.gc_maxlifetime', (int)SESSION_TIMEOUT_CATALOG);
    }
    if (preg_replace('/[a-zA-Z0-9,-]/', '', session_id()) != '')
    {
      zen_session_id(md5(uniqid(rand(), true)));
    }
    $temp = session_start();
    if (!isset($_SESSION['securityToken'])) {
      $_SESSION['securityToken'] = md5(uniqid(rand(), true));
    }
    return $temp;
  }

  function zen_session_id($sessid = '') {
    if (!empty($sessid)) {
      $tempSessid = $sessid;
      if (preg_replace('/[a-zA-Z0-9,-]/', '', $tempSessid) != '')
      {
        $sessid = md5(uniqid(rand(), true));
      }
      return session_id($sessid);
    } else {
      return session_id();
    }
  }

  function zen_session_name($name = '') {
    if (!empty($name)) {
      $tempName = $name;
      if (preg_replace('/[a-zA-Z0-9,-]/', '', $tempName) == '') return session_name($name);
      return FALSE;
    } else {
      return session_name();
    }
  }

  function zen_session_write_close() {
    return session_write_close();
  }

  function zen_session_destroy() {
    return session_destroy();
  }

  function zen_session_save_path($path = '') {
    if (!empty($path)) {
      return session_save_path($path);
    } else {
      return session_save_path();
    }
  }

  function zen_session_recreate() {
    global $http_domain, $https_domain, $current_domain;
      if ($http_domain == $https_domain) {
      $saveSession = $_SESSION;
      $oldSessID = session_id();
      session_regenerate_id();
      $newSessID = session_id();
      session_id($oldSessID);
      session_id($newSessID);
      session_set_save_handler('_sess_open', '_sess_close', '_sess_read', '_sess_write', '_sess_destroy', '_sess_gc');
      $_SESSION = $saveSession;
      if (IS_ADMIN_FLAG !== true) {
        whos_online_session_recreate($oldSessID, $newSessID);
      }
    }
  }
btw, yes, I saw the Keep Cart addon. I should have mentioned that. I had decided that was not a good choice for me because there is no support thread or any discussion about it in the forum and my concern it could result in unanticipated Zen Cart behavior.