My _guess_ is as follows: The electric field accelerates ions that happen to be present in the surrounding air. If there is sufficient acceleration, then when these ions happen to bump into other molecules, they will have enough energy to ionize those other molecules. As air density decreases, the 'mean free path' (distance that air molecules travel between collisions) increases. This means that any ions will have a longer time to accelerate and will reach higher speeds, and thus be more likely to ionize molecules that they hit. If you reach the point where each ion (on average) produces more than one ion prior to losing its charge, the you get an arc.
-Jon