The air in the cave will come to equilibrium with the partial pressures of gasses in the water, which itself is in equilibrium with the atmosphere. It's not as closed as system as you think, even though it probably wouldn't outgas oxygen as fast as the divers were metabolizing it.
This is a really interesting point. How big would a cave need to be in order to support the oxygen requirements of a single human? I assume surface area of the water is the important factor?
