Upvote:3
Delta did not cause you to be late. Delta had no control over whether you were late or not. Therefore Delta has no responsibility to refund you money for a problem that was outside their control - any more than they would be responsible if you checked in late because your bus was late or your car broke down.
The people who caused your lateness were you (for not checking in at the recommended time) or immigration - but immigration were almost certainly just doing their job and not at fault.
Sometimes stuff just happens.