The Airport would have to be open for the following scenerio
A Britsh Airways flight is schedualed to leave London at Friday 6am for Tel Aviv. However there is a delay and the flight cant leave until 12 noon meaning it will arrive in Tel Aviv After Shabbos Starts. If you close the Airport, British Airways will be forced to put in a hotel and feed all the passengers and crew in London for the 200 or so passengers costing them alot of money. They will then decide not to fly to Israel, Most airlines would decide to do this as well because they dont want to lose money either.
You can say Shabbos trumps this and that is correct, but British Airways doesnt care