This is an interesting story, but biologically the story plays out a bit differently.
Biological systems are in dynamic equilibrium, an individual system can involve an enzyme and its receptors, say cortisol and
glucocorticoid receptors. But these receptors are expressed in many different cellular systems, many of which are not really considered to be merely associated with 'stress responses', but also basic functioning of the body. There are both feed-forward and feed-back effects on both the enzymes and receptor expression, all of which have a tendency to keep the system within particular bounds. What happens when something like cortisol is expressed at a greater than normal level over a period of time is that these systems exert negative feedback effects. If that is not enough to shift the system back to a normal range, then the receptor (gene) expression itself will generally shift, often based on self-feedback effects. So the GR expression in the other systems may be reduced to maintain overall homoeostasis of those systems.
It is not merely an oversimplification, but a mistake to assume that cortisol 'depresses' the immune system, in fact cortisol actually increases immune system function, it is simply that it shifts it from a neutral functioning to a mostly anti-inflammatory response. (but I too am oversimplifying here)
Again, there is a balance between enzyme and receptor, so a lower level of enzyme would be expected to be associated with a higher level of receptor expression. What should also be noted is GRs themselves can actually stimulate an anti-inflammatory immune response directly without forming a complex with cortisol. So one explanation for low cortisol may be the immune system shifting towards a more direct anti-inflammatory response.
Organic systems don't magically become 'exhausted' as you might imagine, due to the many feedback effects. Damage to the gland will typically be due to trauma, e.g. physical trauma, infection, autoimmunity etc.. A substantial amount of biological systems would have to become dysregulated for the gland to go into some sort of runaway feedback loop and become exhausted/damaged as a result.
Cushing's disease describes the case where a tumor of the pituitary lead to increased ACTH expression and corresponding increases in cortisol expression.
Most ME or CFS patients do not show evidence of the gland itself being damaged, though there probably are cases where damage may have occurred, likely due to the initial acute infection.
Neuroendocrine studies have shown that the low expression of cortisol is likely due to a low expression of vasopressin (which is also associated with orthostatic hypotension).
The switch between high cortisol and low GR expression (the chronic stress pattern) towards low cortisol and high GR is yet to be explained.
In terms of the abnormalities resulting from the system moving towards (dysfunctional) steadystates, the only respectable approaches so far have been proposed by Broderick and colleagues.
http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000273
And a more comprehensive followup based on hp gonadal axis, not merely hpa:
http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084839
(note that most of the models predicted in the second paper actually described high-cortisol states except for women in the ovulation phase. I daresay this suggests that the model is flawed)
However, other studies have not found the same patterns of expression proposed by the model and I don't think these models fully appreciate the dynamic nature of biological systems - the ranges given in the models would actually suggest that although the body may temporarily reach such steady states, expression levels could often exceed those levels and return to the other steady states. (persistence is not satisfactorily explained)
For example, a recent study on gene expression post-exercise found that GR receptor expression went from normal levels (no difference to healthy controls) to very high levels post-exercise. This large dynamic range is not really captured or explained by the above models.
My personal hypothesis is that the neuroendocrine response observed are simply response to dysregulations elsewhere which cause ongoing cellular oxidative stress which results in higher GR expression as a more direct response.
This shift towards a GR rather than a cortisol response could also be part of compensation if the oxidative stress itself is triggered by some sort of auto-immune loop. I also note that many of the neuroendocrine observations (mild hypocortisolism, GR expression patterns etc) are mirrored in autoimmune conditions such as RA.
