As far I know the power electricity is flow of electrons from anode to cathode of the battery. So basically the electrons flow through the circuit and return to cathode. Why can't we reuse these returned electrons to create an infinite battery ?
The problem is energy. Actually, for almost any physics problem, the answer is 'track the energy'.
In a battery, it's the potential energy of the chemicals, their ability to do work by changing to other chemicals with a different electronic arrangement and lower energy, that provides the energy to push charge round an external circuit. Once all the high potential energy chemicals have turned into low energy ones, no more work can be done.
If you want to keep pushing electrons round the circuit, re-use the charge that returns (so to speak), then you have to keep supplying energy. You could supply mechanical energy to a generator, thermal energy to a Peltier module, or chemical energy in the form of oxygen and a fuel to a fuel cell. These will all make 'infinite batteries' according to your definition, and the last is a chemical battery.
The short answer is, chemistry. Those electrons don't go back to where they came from, they go to a different part of the battery, essentially. All the electrons that leave the battery are the product of a chemical reaction, and once the reagents are used up and the reaction's run to completion, you can't get any more out.
Chemical reactions of the reduction/oxidation (or 'redox') variety always involve the transfer of electrons. It's just that in this case, the battery's construction forces the electrons to take the long way around.
Short answer: Energy has to drive the flow of electrons in the first place. A different kind of energy, like chemical energy. Chemical energy is what pushes the electrons, imparting energy into the flow of electrons. That energy gets used up when we power something. The electrons flow back to the battery but the energy doesnt. The battery has a finite supply of energy in it stored in chemical form.
All reaction in life generates heat, the heat is the result of used up energy correct? When electric charge runs though a wire a small amount of heat is being released this is because everything on earth has a small amount of resistance so even though electricity travels through conducting objects it still has to fight resistance that the object obtains.
That process generates heat which is energy lose. So when electricity travels out of a battery and through a conducting object small electric signals (heat) is being released into the air. This process essentially drains the battery. So basically you can't have an infinite battery unless you have some form of retaining the energy lost and reusing it.
This is my theory in a nutshell. If you want me to elaborate on your question please let me know.