Question

Do mechanical waves lose energy as they travel through a medium? Why?

Answer 1

Yes.
Mechanical waves do loss energy while they propagates through a medium.
This happen due to dissipiation of energy s heat, sound or any other form of losses.
Take the case of sound waves;
As it travels, a sound wave's energy is slowly lost as heat. This happens because the molecules of the medium through which it is travelling knock against each other as they transmit the sound wave energy.