Well I'll be darned... I could SWEAR my iPad air wasn't making this noise before, but recently it's started doing it too. If I lift the smart cover and place it on the iPad's back side, it'll click, and then it will do it again when I close the cover on the screen. Also, the smart cover WILL stick to the back of the iPad casing after the click happens.
On top of this, there even seems to be a brief period of resistance or hesitation when I close the cover, as if the two poles of the magnets between the cover and the iPad are matched up to repel each other... then when the iPad "clicks," the cover switches from repelling to attraction, and snaps right into place. Kind of like the magnets in the iPad have come loose and flipping back and forth with the cover.
I'm debating whether I want to bring it in though. I don't have any other issues with it, yet.
Also, I still have my old iPad 3 and recently sold off my iPad 2. Neither of those do this clicking behavior.