I think people over-estimate how easy it is to shoot down the drones. Let's say there's a drone, and a guy (police, soldier, security) with a shotgun who sees it. The guy aims the shotgun, but the operator of the drone notices (either because they chose a good vantage point, or have good cameras, or spotters who help them, or whatever), so they zips the drone away out of sight, say, to the nearest trees, and lands. Sure enough, searchers are directed to where the drone vanished to, but I guess there's enough time for the operator to collect the drone and scamper away – it's a large area, difficult to search, with a vast array of hiding spots.
If the operators are really clever and it is a targeted attack specifically to shut down the airport, they get a gang of people with specific purposes (spotters for observing countermeasures, pick-ups for the drone, etc.)
And no, I'm not a terrorist, and never planned to do anything remotely similar to that. Just a simple scenario that pops up within seconds. I should write a thriller about that (if anyone does, I have a post to claim my rights ;) ).