Voltage-gated sodium ion channel proteins open in the next patch of membrane, allowing sodium ions to flood into the axon by diffusion, generating new local currents
During the refractory period, the membrane is unable to generate a new action potential as voltage-gated sodium ion channel proteins are closed and cannot be opened
The problem with non-myelinated axons is that the passage of an action potential is rather slow.
This is because the whole length of the cell-surface membrane needs to be progressively depolarised to pass an impulse from one end of an axon to another.