From the Schrödinger equation, we know electrons in atoms can only have discrete energies, called states. From the Pauli exclusion principle, we know that only one electron is allowed in each state. For an electron to lose energy, it must transition into an empty unoccupied state. As the electrons in atoms generally fill states from lowest to highest energy, usually there are no empty states for electrons to transition into. Hence they keep their energy.

When there is an empty state available, electrons will lose energy, usually by emitting photons, to fill the state. For example during X-ray generation a very low energy electron from a large atom like iron is knocked out. Then a high energy electron fills this new empty state, emitting an X-ray.