Ambiguity about the relation between membrane potential and concentration gradient in neuron cells
I interpret your question to be roughly: "the equilibrium potential is based on a concentration difference, but as ions move to create the electric potential, the concentration difference is changing. Why doesn't this in turn change the equilibrium potential such that the concentrations become equal and the potential becomes zero?"

If I'm correct...

The answer to your paradox is that very few ions have to move.

The number of potassium ions that would have to move across the membrane to establish the resting membrane potential is tiny. Electrical forces are very very strong. The imbalance in ions doesn't affect the concentrations inside and out appreciably.


  For a typical cell, 1 microcoulomb of charge (6 × 10^12 monovalent ions) per square centimeter of membrane, transferred from one side of the membrane to the other, changes the membrane potential by roughly 1 V. This means, for example, that in a spherical cell of diameter 10 μm, the number of K+ ions that have to flow out to alter the membrane potential by 100 mV is only about 1/100,000 of the total number of K+ ions in the cytosol.


from Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K., &amp; Walter, P. (2002). Ion channels and the electrical properties of membranes.

However, because membranes are also a little permeant to sodium, and because action potentials and synaptic transmission allow some additional ions to flow across the membrane, if you gave infinite time, eventually the ion concentrations inside and out would equalize, and the membrane potential would eventually be zero. The sodium-potassium pump solves this problem by continuing to keep potassium high and sodium low inside the cell.