So you have a fixed time when each questionnaire is sent out?
They you can simply add a time limit to your questionaire:
if (time() > strtotime('2018-05-15 20:00:00')) {
buttonHide();
text('too_late');
pageStop();
}
If the time is not fixed, you may have to work with the MAILSENT variable which, however, is either unavailable or rounded if your email addresslist is not personalized, but pseudonymous or anonymous.