Falling is an extremely awkward, under-defined part of the rules. That said, the basic rule for provoking an attack of opportunity is pretty simple:
Moving out of a threatened square usually provokes an attack of opportunity from the threatening opponent. There are two common methods of avoiding such an attack—the 5-foot step and the withdraw action.
Moving out of a threatened square usually provokes. Since the warblade is leaving the threatened square, he is moving out of it, and he is going to provoke.
You could argue that “moving” refers to particular, intentional actions taken by creatures to move themselves, and that falling does not count. But the rules use the word “move” or “moving” to refer to any kind of movement, whether it’s from a move action or not, all the time, so I think this is a weak argument. For example, a creature shoved out of a threatened square with a bull rush explicitly provokes. So does a creature carried out of a threatened square by a mount (at least, probably). So falling should as well.
But no part of the rules directly addresses this situation, that I can find.