During the course of an action potential, the membrane potential rapidly rises and reaches a peak of about 40 mV before falling to about -75 mV. What causes the fall in membrane potential

This is because the voltage gated sodium channels which opens for the influx of sodium ions, which caused  increased postivity of the axoplasm closed, with simultaneous opening  of potassium channels.

Therefore depolarization stopped, thus  propagation  and transmission of action potential (caused by depolarization) which cause the reversal of charges in the membrane (making the axoplasm  more negative) for the voltage rise to 40mV also stopped.

In addition the  simultaneous opening  of voltage gated potassium channels caused K+ to leave the axoplasm to the external environments. This makes the inner membrane to be negative further lowering the potential, to -75mv. This is  re-polarization.

Explanation: