Well I don't automate workers, so this definitely wasn't the issue.
Definitely not automated Workers, and not an enraged unit either. The proof: It's the city a unit is airlifted FROM, not TO, that counts. You can airlift only one unit per turn FROM a city, but there is no limit on the number of units you can airlift TO a city. Selecting a unit in one city and mousing over cities on my continent, I would see the green cursor that means airlift is available. Mousing over the city on the other continent while having the same unit from the same city selected results in a grey cursor, i.e. airlift not possible.
More evidence: No units of mine exist on the other continent, which they would even if they had automatically been airlifted through. And this problem has been consistent over several different turns - you'd think if for some reason the airlift was unavailable on one turn, it should be available on another.