Can we recover infinite energy from the gravity between point particles?

Suppose that we have two point particles which attract each other. If we use ropes to lower them very close to each other, can we recover more energy than what was the mass-energy of the two particles?

If that were possible, it would conflict with conservation of energy.

           e- ●   ----->        <-----   ● e+

If the particles are an electron and a positron, then lowering them to a distance ~ 10⁻¹⁵ m would recover more than 1 MeV of energy. Nature has solved the problem by letting the pair to annihilate each other before we can recover too much energy.

If we have a Schwarzschild black hole, and use a rope to lower a test mass m to it, then at the horizon we have recovered the energy m c². The infinite force at the horizon prevents us from lowering the test mass even lower, and recovering too much energy.

However, in our own Minkowski & newtonian gravity, the force at the horizon is not infinite. Does our model allow us to recover too much energy?

No. The gravity charge of the system decreases as we recover more energy. If we could recover the entire mass-energy of the system, then the remaining gravity charge would be zero, and there would be no gravitational attraction left to do work.

This is the familiar rule that one must subtract the binding energy from the mass of a system.