Note how you haven't pointed to a single thing that's bad with his post, but nonetheless managed to sling several condescending accusations (has no clue, quasi-poetic, nonsense) at him...
And all that for a point where he doesn't even pretend to give any specific explanation or causual relationship or anything, just wants recap with a description of the outward appeareance of the phenomenon, precisely to show that we have no clue about it yet:
"It looks like sleep is somehow renewing these people's depressions. As if depression is caused by some injury during sleep, heals part of the way during an average day (or all the way during an extra-long day of sleep deprivation) and then the same injury gets re-inflicted during sleep the next night".
In TFA this is not an explanation of what happens, but an "it looks as if somehow" to highlight exactly the current lack of an explanation, an explicitly presented as such.
The first few times I happened to do it was not because I was aware of the link (20 years ago nobody wrote about it). It was by accident because I've stayed up so late that dawn surprised me during a night of insomnia. So it made more sense to just power through the day with coffee rather than mess up my sleep pattern. It certainly works for me like some kind of reset.
She said it was for the patients whom were brought in because they just tried to kill themself’s, or told admittance they wanted to die.
I had the idiotic idea I could cure my dysthymia (Minor depression) by sleep deprivation, and it didn’t work at all.
It is generally accepted that the negative effects of sleep deprivation last longer than a day too. If you are sleep deprived you can't 'catch up' by sleeping in for a night or two (for example on the weekend).
I can give another off-the-cuff alternative: sleep deprivation reduces self-awareness, and thus self-report of depressed feelings. It might be that at this point the "brain" is more susceptible to treatment, but that's an entirely different matter.