A bouncing ball loses some of its energy at every bounce. The ball and the Earth collide, and during this collision momentum and kinetic energy are transferred. If the kinetic energy of the ball before the collision does not equal the kinetic energy of the ball after the collision, the ball cannot bounce back to the height of previous fall because it does not have enough kinetic energy to convert to potential energy.
Moreover, simple harmonic motion requires a force whose magnitude is proportional to the displacement and whose direction points towards the equilibrium point of the motion, called a restoring force, and this is not the case for a bouncing ball. The ball is under the influence of gravity during the entire process and the repulsive forces during the collision. Neither are restoring forces, so a bouncing ball's motion is not considered simple harmonic.
