If F(action) =F(reaction), why doesn't a ball bounce to its original height? This might seem like a very absurd/ridiculous question, but this question suddenly popped on my head a few days ago. Is it that I'm missing something as I haven't reviewed this topic for quite a while?

So my assumption is if an object exerts a force equal and opposite to the object which acts on it, shouldn't a ball dropped from a certain height exerts a force (m.g) on the ground and it reacts back by pushing the ball upwards and thus sending it back to its original position/height?
I then thought for a while and realized this would be a contradiction to the Energy Conservation Law and it wouldn't make any sense anymore. I've come to known that I've definitely forgotten something. Any help would be greatly appreciated.
 A: Yes, if the ball were to bounce elastically(no energy lost in the deformation of the ball) and there was no atmosphere(vacuum space around Earth) the ball would reach the initial height.
It is very useful in this situation to answer in terms of momentum and energy conservation. In real life the collision of the ball on the ground is not perfectly elastic, that means that some energy is lost in the form of heat and deformation of the ball. 
Also, the initial energy of the ball is $mgh$, with m being the balls mass, g the gravitational field on earth and h being the heigh(assume h=0 the Earths surface). This energy is converted to kinetic $1/2 m u^2$. From that you can deduce the momentum of the ball and apply momentum conservation. Depending on the energy loss due to impact you can calculate the new height that the ball will reach when it bounces.
Does that help?
A: The reaction force is not equal to mg because the ball is being accelerated, in addition once the ball leaves the floor there is no longer a force acting on it. When you drop the ball the force is mg all along the trajectory, even when going up. There is no reason why the reaction force should bounce the ball back to the original height. It will only happen when there is conservation of mechanical energy.
A: This happens because some energy that the ball had initially carried gets lost in the form of heat some energy goes into the ground and the atoms over there begin to vibrate faster and some energy goes into the atoms of the ball and the begin to vibrate faster.
But if we can create a situation in which no energy goes in form of heat and that the ground in infinitely heavy then the ball will reach its original height
A: The tax man takes his cut in energy in the form of heat.  Accelerating electrons emit photons.  When the ball hits the earth the sudden deceleration which is a reactionary acceleration causes the electrons to emits photons and tax the bounce back energy so the ball doesn't go back to the same height.  If the ball is flexible like a basket ball then the flexing of the walls will add to the problem.
