My flight is delayed. Does the airport close at night for departures?

Yes and opens at 4am

Im asking if the airport is operating 24hrs or whether it closes at night. I know my flight is still scheduled but it keeps getting delayed more and more so I would like to know whether there is a cut off time after which flights have to depart next morning.

You should check with your airline. It's open if flights are scheduled. If you have a connecting flight, definately check with the airline directly

I don't understand what it is you're asking.