Does the emf of an electrode potential change over time?
Yes. Remember that the standard electrode potentials are for 298K at 1 atm of pressure and 1N concentration of reagents. As the concentration of ions to be reduced at the cathode decreases the emf will fall as well and is reflected in the Nernst equation.$$E_{cell} = E^\circ_{cell} - \frac{RT}{nF}ln(Q)$$