A simple question about the direction of a chemical reaction
Before I talk about the chemistry, I will use an analogy from physics. If I drop a piece of chalk, it falls down. It does not at some point later "fall up" again. However, the atoms inside the piece of chalk do go up and down a bit because of thermal vibration. The chalk does not start jumping up because these vibrations are random rather than synchronized.


  Why does not the reaction spontaneously reverse once again forming pure Zn and H2SO4 molecules? 


If you are asking why at no time the mass of elemental Zn (metal) increases again, it is because there is a strong driving force toward turning the reactants into products for this specific reaction. If you are asking about individual particles, it turns out every now and then, the reverse reaction does occur (this is true for all reactions and is called micro-reversibility). 

For some reactions, this back and forth results in the reaction not going to completion. Instead, these reactions may reach an equilibrium where reactant and products are present, and the forward and reverse reactions go on at the same speed so nothing seems to change (this state is called a dynamic equilibrium).

In the reaction you are asking about the driving force forward is too large, and one of the products continuously "escapes" from the reaction mix, so the reaction goes on until one of the reactants is used up (goes to completion rather than reach equilibrium).

In any reaction, reversible or not, once the reaction reaches equilibrium or goes to completion, it does not spontaneously go in the opposite direction unless something changes (add materials, change temperature, do work).