Neurotransmitters are exchanged via synapses, not ions. And they get taken back up (a process creatively named reuptake). The basis of some pharmaceutical drugs (especially anti-depressants) is that they inhibit reuptake, allowing the neurotransmitter to hang around in the synapse longer to greater effect.
K/Na both leak out of the membrane itself, though, and little protein pumps powered by ATP act to keep up with the leaking. I'm not sure how Na/K leave the brain or body.