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[OngBonga]

Rather than assuming an infinite mass, it's better to just measure h as a fixed point from the ground, which means h moves if the ground moves. That essentially fixes the ground in the sense that it makes it mathematically immovable, while not complicating gravity and energy!

The (electro)magnetic field is perfectly elastic. Any energy put into deforming it is given back in full.

This is a really good point.

the deformation will cause some internal heating, which is energy lost from the mechanical interaction.

At least heat loss will be reduced to the bare minimum blackbody radiation, seeing as we're in a vacuum and we're assuming the ground is in thermal equilibrium with the ball!

[MadMojoMonkey]

At least heat loss will be reduced to the bare minimum blackbody radiation, seeing as we're in a vacuum and we're assuming the ground is in thermal equilibrium with the ball!

My point is that the internal energy of the ball has gone up, and that energy came from somewhere.

If anything that is not the mechanical energy goes up, then the mechanical energy must go down to compensate, such that total energy is conserved.