When we look at a superconductor, the conductivity is infinite. And when we apply a potential difference across the ends of the superconductor, the electrons have to start accelerating because there is no resistance. But once electrons start accelerating, they must produce electromagnetic waves which can lead to power losses. Then why is it that books mention that there are no power losses in a superconductor?
Superconductivity comes from a condensation of Cooper pairs into a super-fluid state. Cooper pairs are composed of two electrons which are bonded by some attractive forces (the origin of the force depends of the materials, but in classical superconductors, the force is electron-phonon interactions). Cooper pairs are bosons (at large scale) even though they are composed of two fermions. That is why they can "condense" in a single quantum state. You can see this like a Bose-Einstein condensation that happens at low temperature and where all particles behave the same and are strongly correlated.
This single quantum state is the ground state of a many-body system with interactions between particles, the particles here are at their minimal energy value (they cannot go lower). Thus, the particles cannot radiate energy even though they are accelerated or decelerated. The analogy with a super-fluid is that the electrons acts like they are a liquid with absolute zero viscosity (this is why there is no resistivity at that point). Technically, once the electrons in a superconductor starts flowing, they can flow like this for eternity even without any applied voltage (experiments were done to test this idea and could only result in a lower boundary for the current lifetime).
There are losses in the situation you describe, as electromagnetic radiation is radiated away. These are not resistive losses, however. That is to say, no energy is lost to heat.
Once you remove the potential difference, however, the current persists. It is in this situation that there are truly no losses. The current remains without any applied potential, and does not decay over time.