Why does the size of an action potential not change?

This consistency in the size of an action potential is due to the properties of the voltage-gated ion channels involved in generating the action potential. When the threshold is reached, these channels open in a predictable manner, allowing sodium ions to enter the neuron and potassium ions to exit, which generates the action potential of a fixed size.

The intensity of a stimulus is coded into the frequency of the action potentials that are generated. Hence, a stronger stimulus increases the frequency or number of action potentials but it does not increase the size of the action potential.