Loss in energy by light after reflections

Energy of light is proportional to its frequency.

The energy of a photon is proportional to its frequency.

The power of a light beam is determined by the photon energy and the number of photons it delivers per unit time.

So if light loses energy on reflecting off a surface then why doesn't it change its colour?

An imperfect reflector causes the light beam to lose energy by absorbing some of the photons, not by changing the energy of each reflecting photon.

Often it does not lose much energy on being reflected. It loses energy on being absorbed. Each reflected photon has the same energy as before.

Some colors may be preferentially absorbed or reflected. So a beam may lose energy and change color when some of it is reflected from a colored surface.

Light may lose or gain energy on being reflected from a moving mirror because of the Doppler shift. Police radar guns work this way. Radar guns are sensitive to very small frequency shifts. An object must be moving at relativistic speeds to have a significant color shift in the visible spectrum.

Keep in mind all observers see light as traveling at the speed of light. Suppose A sees a light of a given color. Suppose B is moving away from A. The light passes A, reflects from B, and returns to A. A would see the reflected light as having a lower frequency.

Light carries momentum, so each photon kicks the mirror. The mirror recoils. So the photon does lose energy on being reflected. For a macroscopic mirror, this is a very small effect. But it is not small when light scatters from a charged particle. Thanks to HolgerFiedler for pointing this out.