Also, will the axon terminals in a given motoneuron ever run out of neurotransmitters to release if they are constantly undergoing action potentials (say in the situation outlined above where a muscle is being kept flexed)? Or is there always enough reuptake to ensure that this could never happen?
Second question: won't happen in the healthy individual/inapplicable.
Anatomically speaking, muscles don't flex, they contract. Joints flex. And muscles never fully relax to the point of zero contraction/zero firing. (The flexion of a joint can be achieved passively, even when the animal is dead.)
First question: depends on effort. Muscle firing during increased, active contraction is a function of effort, as muscle contraction is increased via rate coding. The stronger a muscle is supposed to contract, the higher the motor unit's firing rate has to become. (I should probably mention the size principle here...) Motor neurons are reported to reach firing rates of a few tens (up to 50) of hz during high effort.
A question you're possibly interested in: for how long can extremely high firing rates be sustained? Or: is muscle failure under sustained extreme effort, corresponding to high firing rates, sometimes a result of motor neuron drop-out rather rather than e.g. ATP depletion at the muscle itself?
Also see this.