Why doesn't Newton's third law mean a person bounces back to where they started when they hit the ground? When we drop a ball, it bounces back to the spot where we dropped it, due to the reaction forces exerted on it by the ground. However, if a person falls down (say, if we push them), why don't they come back to their initial position where they started their fall?
According to Newton's 3rd law of motion, to every action there is always an equal but opposite reaction. If we take the example of ball then it comes back with the same force as it falls down. But in the case of a human body, this law seems not to be applicable. Why?
 A: 
If we push a person and he falls down then why doesn't he come back to its initial position. Although according to Newton's 3rd law of motion: To every action there is always equal but opposite reaction.

That's not a correct statement of Newton's third law.
Newton's third law of motion actually says: "If one object exerts a force on another object, then the second object also exerts a force on the first object, which is of the same magnitude but in the opposite direction."
So in this case, what Newton's third law is saying is: "If the floor pushes up on a person with a certain amount of force, then the person pushes down on the floor with the same amount of force." From this, there's no reason to think that the person would bounce back to his initial position.
A: Newton's third law just says when the person is hitting the floor the force the person exerts on the ground is equal to the force the ground exerts on the person at all times. i.e. all forces are interactions.
Newton's third law does not say that all collisions are elastic, which is what you are proposing. When someone hits the floor, most of the energy is absorbed by the person through deformation (as well as the floor, depending on what type of floor it is), but there is barely any rebound since people tend to not be very elastic. i.e. the deformation does not involve storing the energy to be released back into kinetic energy. Contrast this with a bouncy ball where much of the energy goes into deforming the ball, but since it is very elastic it is able to spring back and put energy back into motion. However, it is unlikely the collision is still perfectly elastic, as you seem to suggest in your question.
In summary, Newton's third law tells us that action-reaction force pairs must have equal magnitudes and opposite directions, but it doesn't tell us anything about what the magnitude of these forces actually are. Your misunderstanding likely comes from the imprecise usage of the words "action" and "reaction". In this case, these words refer to just forces, not entire processes. You can get some confusing questions if you don't understand this. For example, why is it that when I open my refrigerator that my refrigerator doesn't also open me?
A: When your body hits the floor, it does receive an equal and opposite reaction force from the floor. But unlike a ball a body is a complex object. So not all energy is transferred back as kinetic energy. Some energy is used to produce sound, some is used to deform your body... etc. I think you are confusing force with energy. Does every ball bounce back the same amount? Newton's 3rd law talks about force only.  More force doesn't always (mostly) equal to more work done.
In your case, if all the force was used to change the body's kinetic energy somehow (which is not realistically possible), then it would have bounced back the same amount.
A: It's true that on the impact the human body experiences a force upwards equal to the force the body exerts downwards on the Earth: $\vec{F}=\frac{\Delta\vec{p}}{\Delta t}$.
Now $\Delta\vec{p}$ doesn't send the body's momentum in the opposite direction, but instead, the momentum change is used to deform the body (breaking bones and other kinds of nasty things) in a way that absorbs the kinetic energy.
When the person jumps on a trampoline (and even then only by approximation) he'' return to the point he started from.
When the person jumps from a small height, in which case he or she can give his(her)self an upward force by stretching his legs in which case he can reach the same height as where he came from, or even higher; in this case though, the energy necessary to return to the same hight comes from the body, which makes it an explosive collision and here we are talking about an inelastic collision.
Some parts may bounce back upwards but are pulled back again by the rest of the body. So all kinetic energy has conversed in other forms of energy. 
So to conclude, this is an inelastic collision where the human body and Earth stick to each other in a nasty way (maybe an elastic ball the person had in his hand when falling shoots up when contact is made with Earth...).
A: Newton's third law states that when a particle applies a force on another particle then the former experiences an equal but opposite force from the other.When a ball hits the ground it comes back due to the fact that it experiences an elastic collsion(that is does not undergo any deformation).Think about a fur ball,will it come back,obviously no,why is that so?This is because when a fur ball collides with the ground(assuming a concrete ground)it undergoes deformation (due to the reaction force from the ground) and the kinetic energy of the ball is used up in deforming the ball.Same is the case for a human being who undergoes deformation on hitting the ground and hence does not come back to it's initial position.
A: Energy is not lost, but it is expended in different ways when different objects collide.
A more visceral statement of these principles:
Drop a rubber ball on the floor.  As it hits the floor it stores up spring energy inside itself, and then bounces back almost as high as the start point, losing only a little energy to friction. 
Drop a hard billiard ball on the floor.  It bounces a bit, but much of the energy gets spent making a dent in the floor.
Drop a sphere of soft clay on the floor.  It goes "splat" - most of the energy is spent pushing the clay out sideways.  (There may be a small crown on the blob of clay on the floor where some of it did bounce back a bit.)
Drop a human being on the floor.  Where does the energy go?  It goes into bruising skin and muscles, bouncing internal organs back and forth, forcing air out of the person's lungs, swear words, etc.  It takes quite a forceful impact to have enough leftover energy yo make a human being bounce enough to see.
The concept of a spherical cow is often used to describe the way real-world objects are simplified to make the underlying physics easier to describe; in this case you seem to be thinking of a spherical person.
