The primary cause of hyperpolarization during an action potential is the delayed closing of potassium channels after repolarization.

- During an action potential, the neuron rapidly depolarizes due to the influx of sodium ions through voltage-gated sodium channels.
- Following this, the membrane potential returns to the resting level in a phase called repolarization, which is mainly driven by the efflux of potassium ions through voltage-gated potassium channels.
- However, these potassium channels do not close immediately after repolarization.
- Instead, they remain open for a short period, allowing excessive potassium ions to leave the cell.
- This results in the membrane potential becoming more negative than the resting potential, a state known as hyperpolarization or the after-hyperpolarization phase.

Key points to note:
- Delayed closing of potassium channels extends potassium efflux beyond the resting membrane potential.
- This causes the membrane potential to become more negative than the usual resting level.
- The hyperpolarized state makes the neuron less excitable briefly, ensuring proper directional signal propagation.

The other options are not correct because:
- Prolonged opening of sodium channels would maintain depolarization, not hyperpolarization.
- Early inactivation of calcium channels primarily affects calcium influx and does not play a major role in hyperpolarization.
- Increased permeability to chloride ions could cause inhibitory effects but is not the primary cause of hyperpolarization during the classic action potential stages.