Movement perpendicular to and away from the earth will convert to potential gravitational energy, which is then released when the ball moves back towards the earth.

In addition, you're assuming that the balls are passive participants. In actuality, from the waves perspective, they are actively resisting being lifted, and actively attempting to fall, limited by their buoyancy in the water. When the wave causes the water to fall away from the balls, they are falling into the water on that trailing edge.

Finally, conservation of energy dictates that that energy does not just disappear. If the energy goes into the ball as movement, something has to stop that movement. That something is going to be either gravity if moving up, or the water itself in any other direction. So the energy is moving from the water, into the ball, back into the water as it resists the ball displacing it to move.

Yes of course these are not perfect processes. Otherwise an undersea earthquake would create a tsunami on all of its coastlines. Energy is lost or made non-coherent in a variety of imperfections, including heat and scattering. In the case of ocean waves, they are typically created and recharged by the wind as they move along.

I mostly wanted to make the point that a wave is not displacing its medium, but simply moving through it. A wave is nothing but water and energy. There's nothing there displacing the water to do work. The water moves around due to the energy, but in a way which is generally neutral in terms of work actually done. A wave hitting the shoreline really just transfers from moving through the water to moving through the land.

Here on earth, a ball resists being lifted due to gravity. It also returns all that energy when it's dropped again.

A wave that lifts a bunch of ping pong balls on it's leading edge, then drops them on it's trailing edge where the energy is returned to the wave, has done net zero work.

Well, let's look at a wave in water. It moves some water around, but in a cyclical pattern that should result in very little actual work being done. The same way that lifting something gives you all the energy back when you drop it.

Maybe you're thinking of this from the perspective of a solid object moving through a medium, where it must spend energy on displacing the medium in order to move? This is where my note regarding the wave being energy is important. It does not have to displace anything to move through the medium, the same way that the heat from your stove doesn't displace your pan in order to heat your food. The energy simply goes through.

A wave doesn't contain energy, it is energy. And it would only lose that energy by doing work, same as anything else. So what work do you think it is doing when it passes through a medium?