The membrane potential is in flux as Local gates open in response to external chemical stimuli throughout the dendrites of the neuron. These gates depolarize or hyperpolarize the membrane potential. These changes are local, graded potentials.
As these local shifts happen, (summation) they are quickly dissipated through leakage channels. Also, The NA+ K+ pumps work to maintain the cell membrane potential. This cycle continues to happen as the normal resting state until enough stimulation is experienced, the threshold is reached, and the AP fires down the Axon relaying the stimulus.