The Passenger Pigeon went extinct because of the demand for squab back east, and the ease with which huge numbers could be harvested with a couple of shotgun blasts. They didn’t come back because of habitat destruction (their big nesting area was over in the Thumb of Michigan somewhere, like the rest of the state it got lumbered out).
True, there were a number of factors, but apparently when they finally realized they were approaching extinction, there were no enough of them left and I think they tried but just could not get them to breed in captivity.