Neurotransmitters would continue to bind and rebind with the postsynaptic receptors, which would continue induction of a signal in the postsynaptic neurons, which would repropagate the initial signal.
The case in drugs that block reuptake transporters (such as in serotonin reuptake inhibitor and norepinephrine reuptake inhibitor antidepressants, and dopamine reuptake inhibition found with cocaine and methylphenidate).