But you have to set the cookie time in admin/preferences/general settings to the number of minutes the cookie will be stored, i.e. "10080" minutes for one week.

if ($op == 'logout') {
$message = '';
$HTTP_SESSION_VARS = array();
session_destroy();
if ($xoopsConfig['use_mysession'] && $xoopsConfig['session_name'] != '') {
setcookie($xoopsConfig['session_name'], '', time()- 3600, '/', '', 0);
}
// clear autologin cookies
setcookie('autologin_uname', '', time() - 3600, '/', '', 0);
setcookie('autologin_pass', '', time() - 3600, '/', '', 0);
// clear entry from online users table
if (is_object($xoopsUser)) {
$online_handler =& xoops_gethandler('online');
$online_handler->destroy($xoopsUser->getVar('uid'));
}
$message = _US_LOGGEDOUT.'
'._US_THANKYOUFORVISIT;
redirect_header('index.php', 1, $message);
exit();
}