If the event horizons ever touch and become one continuous surface, their fate is sealed - the two black holes will merge all the way in. They can never separate again, no matter what.
There are several possible ways to explain it, with varying degrees of rigorousness.
An intuitive explanation is that escape velocity at the event horizon equals the speed of light. But nothing can move as fast as light, not even a black hole. In order for the two black holes to separate, parts of one would have to "escape" the other, or move faster than light, which is impossible.
EDIT: Another intuitive "explanation" (a.k.a. lots of handwaving) - inside the event horizon, all trajectories lead to the center. There is no possible path from any place within the horizon to the outside. Whichever way you turn, you're looking at the center. Whichever way you move, you move towards the center. If the event horizons have merged, for the black holes to split up again, parts of them would have to move "away from center" (or away from one of the centers), which is not possible.
All of the above is about as "rigorous" as "explaining" general relativity with steel balls on a rubber sheet. It's just metaphor.
More rigorously, see this paper by Stephen Hawking:
Black holes in general relativity
As time increases, black holes may merge together and new black holes may be created by further bodies collapsing but a black hole can never bifurcate. (page 156)
EDIT: Event horizons don't really "just clip each other". Perfectly spherical event horizons are a theoretical abstraction (a non-rotating black hole in an otherwise empty universe). In reality, anything near a BH will deform the event horizon, which will "reach out" towards that mass. If it's a small mass, the effect is negligible.
But if two black holes get close to each other, the EHs become egg-shaped, as if trying to touch each other. If they're close enough, then eventually a very narrow bridge will form in between, and the EHs will merge. At that moment, the full merger is decreed and will procede with absolute certainty until it's complete.