This assumes that you aren't changing the default Zend_Auth namespace. If you are then update my code below to reflect your defined namespace.
PHP Code:
$authSession = new Zend_Session_Namespace('Zend_Auth');
$authSession->setExpirationSeconds(3600);
You will want to insert that into your authenticateAction() function right after the user is determined to be valid. Below is your code showing you where the snippet above should be roughly.
PHP Code:
if (!$result->isValid()) {
// Authentication failed; print the reasons why
foreach ($result->getMessages() as $message) {
echo "$message\n. Click <a href='".$this->view->baseUrl."/'>here</a> to try again";
}
} else {
$authSession = new Zend_Session_Namespace('Zend_Auth');
$authSession->setExpirationSeconds(3600);
$dbAdapter = Zend_Registry::get('dbAdapter');
...