Q:

Can neurotransmitter depletion cause short-term drug tolerance?

I'm curious to know if neurotransmitter degradation factors into drug tolerance and neural conduction and, if so, to what extent. As I recall from textbooks I read as an undergrad, one mechanism of drug tolerance works by increasing the necessary thresh-hold at a synapse such that larger concentrations of neurotransmitter or more-frequent action potentials in the upstream axon were required to depolarize the membrane and propagate the signal. It seems to me that the same effect would occur if there were fewer available molecules of the required neurotransmitter.
Does over-stimulation of a neural pathway (through the use of a drug or other stimuli that up-regulates a given neurotransmitter) shorten the half-life of the neurotransmitters it uses? 
Could a diet which is poor for necessary precursor nutrients cause a person's neurotransmitter concentrations to drop and reduce signaling along specific neural pathways? 
Could lack of sleep or other physiological stressors have a similar effect? 
I am not a neuroscientist so please correct (and forgive) me if I'm using any terms incorrectly or am flat-out wrong in any of my assumptions.

A:

As I recall from textbooks I read as an undergrad, one mechanism of drug tolerance works by increasing the necessary thresh-hold at a synapse such that larger concentrations of neurotransmitter or more-frequent action potentials in the upstream axon were required to depolarize the membrane and propagate the signal.

Yes - usually through a reduced expression of receptors on the surface. Increasing the drug dosage merely increases the probability that one of the molecules will find the receptor. Chronic exposure of increasingly large doses can dramatically reduce receptor expression. In time, sans the drug, the receptor count will climb back up. 
This is why a common cause of chronic drug addicts who have just gone through rehab is overdose: After months in rehab or free of a drug they immediately go back to the amount of drug they were doing before rehab - with some severe side-effects at the least, death at the worst.

Does over-stimulation of a neural pathway (through the use of a drug or other stimuli that up-regulates a given neurotransmitter) shorten the half-life of the neurotransmitters it uses? 

No. The half-life of a neurotransmitters is not a major concern; your body will construct them from stored resources if necessary, and healthy neurons have a significant store of neurotransmitters to prepare for multiple firings.
A neuron can be artificially over-stimulated and the neurotransmitter pool emptied (or all the neurotransmitters is bound to its receptor) - but only for Ach receptors at neuromuscular junctions. It hasn't been observed naturally, and not for other types of synapses. This does not result in the muscle no longer responding, but rather it will not respond any faster.

Could a diet which is poor for necessary precursor nutrients cause a person's neurotransmitter concentrations to drop and reduce signaling along specific neural pathways?

Yes, but by that point you're not in good shape, if not courting death. Neurotransmitters are either very common in the diet - like ions - or are constructed from very common constituents of a normal diet - like Glutamine, the most common amino acid.
It would not be a therapy to treat drug addiction.

Could lack of sleep or other physiological stressors have a similar effect? 

You would die of lack of sleep first. Your body generally keeps a 30 day supply of absolutely essential vitamins and minerals, and will easily digest itself for precursors to construct neurotransmitters out of.
I have not heard of any physical or mental stress which has reduced the amount of neurotransmitters released into the synapse beyond absolute starvation or artificial scarcity.

