The gate agents usually advises you to stay in the vicinity of the gate area during a delay unless they figure out that its going to be over an hour or so. Also it helps to have the Southwest App and App in the Air on your phone and Flight Aware to ensure you don't miss the new boarding time. Also having access to the Flight Information Display also helps.

In the end its incumbent upon the passenger to get updates and to be ready for boarding at a moments notice. Miss boarding the delayed flight then the airline could say you were not present for boarding and that you were called numerous times for boarding then you could be in another limbo.