I have found more times than not that its the automated system DL has in place and not the agent. I have been boarding an aircraft countless times during irops where it gives the weird beep and they have to rebuild my reservation, all because an agent elsewhere protected me on a later flight and the automated system didnt like that.

I also hear grumbling a lot of times from agents that whatever group rebooks passengers in the event of a cancellation, do it horribly.

Ive been so many places that i cant remember where this one happened, but about a month ago, we had a late inbound aircraft and the agent at the gate was talking to someone on the phone about helping them rebook a flight since my original flight was going to be so late everyone was going to miss their continuing flight. Gist of the story (after talking with the agent) he told me that they wanted to wait until the aircraft was off the ground before they started rebooking anybody. Talk about bass ackwards.

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Look at your itinerary (if by ticketing agent you mean at the airport) it will say "Interrupted travel" at the top and a back up flight right underneath your original flight. That would be your confirmed protection.