Why is a batterys potential not constant

We define the emf as having a positive value and, strictly, it is always determined at equilibrium. 

The two currents (for anode and cathode) are generally different. Neither of them is related to potential in a linear way. 

A healthy battery for powering a Walkman or radio has a voltage of about 1.5 V. In the terminology of batteries, this value is called its open-circuit potential, but an electrochemist talking in terms of cells will call it the emf. This voltage is read on a voltmeter when we remove the battery from the device before measurement. But the voltage would be different if we had measured it while the battery was, for example, powering a torch. 

Ohm s law, Equation (7.16), describes the difference between the emf and a voltage under load  

In summary, we say the voltage of a cell is the same as a cell s emf if determined at zero current. From Faraday s laws of electrolysis, this criterion implies that none of the compositions within the cell can change. In other words, a cell emf is an equilibrium quantity. 

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