The amount of energy the ball looses is a function of the height before it hits the ground. The shorter the height the less energy. So the answer is No. The amount of energy the ball has each time it is in the air is also a function of the height. It is known as potential energy. Again the higher the ball is the more potential energy it will have. Potential energy also occurs in the spring of the ball and the earth right before it bounces up. The first amount of potential energy was given to the ball when it was first lifted off the ground against gravity. Usually this energy is supplied by a person. Each time the ball bounces some of the energy is release as friction and force of hitting the ground going into the ground and the ball causing some damage. The remainder becomes potential energy as it goes back up into the air.
The amount of energy that is lost depends on how far the ball is squeezed as it hits the ground. Some of this compression is turned into heat so the amount of energy available for the rebound is less than the amount that went in. When dropped from a height, the amount of compression is great, so the amount of heat generated (and compression lost) is great. As each bounce is lower, the amount of compression is less, so the amount of energyh lost is less. In other words the amount of energy lost is proportional to the energy coming in, which gets less and less with each bounce.