During action potential propagation in an unmyelinated axon, why doesn't the action potential suddenly "double back" and start propagating in the opposite direction?

The region fo the neuron is in the refractory period as the sodium channels are inactivated.

Explanation:

A propagating action potential always leaves a trail of refractory membrane in its wake. The trailing membrane takes some time to recover from the action potential it just experienced. This is largely because its voltage-gated sodium channels are inactivated. By the time this membrane segment is ready to (re) generate another action potential, the first propagating action potential is long gone.