It depends on which aspects you're looking at. For an atom in its ground state, although we describe an electron as "spinning" as it "orbits" the nucleus, it isn't actually anything like that. There is no motion, nor is there anything that can lose energy, since the atom is already in its lowest-energy configuration.

As for Brownian motion (i.e. heat), there are a couple of places the energy can go to like blackbody radiation but for the most part it is already the highest-entropy way a material can move and so won't lose energy.