What causes cooling CMB photons to lose energy for 13.8 billion years without slowing down?
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your question has its specific and clear answers in the framework of the theory of general relativity, where you describe photons moving on the background of an expanding universe, however, it is not that simple to explain the Einstein equations etc. without going very deep into the theory. A photon always travels at the speed of light, like all massless particles; in a way (only in a way!), one could say that the photon does not lose speed, but it loses energy to the gravitational field of the expanding universe. The effect is that the energy of the photon E = hbar times f gets smaller, its wavelength gets larger; but the speed remains the speed of light.
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