Final answer:
Drugs that hyperpolarize an axon increase the membrane potential, making it harder to reach the threshold for an action potential, thus reducing the nerve's sensitivity to further stimulation.
Step-by-step explanation:
Drugs that hyperpolarize an axon would indeed make the nerve less sensitive to further stimulation. This is true because hyperpolarization increases the membrane potential, making it more negative than the resting membrane potential. This increased negativity makes it harder for the neuron to reach the threshold needed to initiate an action potential. Therefore, the nerve becomes less responsive to stimuli as it is more difficult to depolarize the neuron sufficiently to fire an action potential.