Theoretically a flight could be delayed forever yes. Practically, as the delays roll, customers who have other flight options will be given them. This is why many flights which are substantially delayed go out with 20% of the original pax.

Although I guess it didn't happen to you, if you are waiting for a delayed flight off-site, be careful if you have checked bags because they may not (probably if not at a hub) take it, and there may be no DL employees in the check-in area at small stations -- even if there are hours before the new departure time but you are after the original baggage cutoff time.