ATLANTA—An airline delayed a Tuesday afternoon flight by 47 minutes after an extended apology caused it to miss its departure slot, requiring a second apology.

"We know your time is valuable," the captain told passengers, entering the seventh minute of a statement about the value of their time.

The original delay involved a late inbound aircraft. By the time the captain had explained the airline's commitment to transparency, the aircraft was ready and air traffic control had given its slot to a plane whose captain had said "sorry" and stopped.

The replacement slot was lost during an acknowledgment of how frustrating the first lost slot must have been.

"We are not going to rush an apology," said an airline spokesperson. "That would suggest we hadn't learned anything."

Passengers received a notification revising their departure time to "following remarks." A flight attendant demonstrated the location of the exits, then clarified that this was informational.

The airline's customer-service system recorded the incident as three successful communications and one flight.

A passenger who attempted to interrupt was thanked for his feedback. Addressing it took another eight minutes.

The plane eventually reached the runway, where the captain announced that the crew had exceeded its permitted duty hours. A replacement crew was on the way. They had been briefed and were sorry.