That looks like real serious effort on both your part and the students part.
I want to say first that you both deserve some positive feedback, ie tell each other that you have put in lot of work and effort and even if it doesn't feel like making progress you really are progressing. Like Edison trying to find good lightbulb filament your trying lots of things and finding the path through trial and error, if you keep at it eventually you will see the light.
https://www.smithsonianmag.com/innov...son-180947786/
So celebrate the journey up the mountain, you can't see the summit yet, but your not at sea level anymore. Go out for tacos maybe? Shoot some balloons? What Cirillo called the unconscious has big impact on performance IME.
Couple things come to my mind after reading that based on my experiences learning and (trying) to teach others. Not limited to shooting.
Personally when I started martial arts I fucking sucked, as in first year in college class taking martial arts class in college taught by the only LEO instructor there I was the absolute worst that drove the teacher to frustration. And we where friends but if I had been graded on meeting any standards for that class I would have earned a F
Not for lack of motivation or lack of interest. I had been studying martial arts on my own from like 5th grade and this was as college freshman. It was something I really wanted to become proficient at.
But I am very much a word person, primarily written word as my main source of information uptake. So learning by watching instructor demonstrate wasn't easy for me, or even when he came and would move my limbs with his hands I still wouldn't grok what I was doing wrong. The issue which I didn't figure out till after that class ended was that there is a lot of internal tensing/bracing of muscles going on that you couldn't SEE when instructor demonstrated and no one said to me because to them it was intuitive.
I don't even remember the epiphany anymore but 6 months after that class when I started taking martial arts from fellow college student that was established martial artist, he had two dojos in the area, I was an average beginner martial arts student instead of the person at very bottom of the curve.
During that same time period, ie my early college years, my history professor recommended me as possibly tutor to two students that were trying REALLY hard but struggling in his class.
I did my best to help them, but I knew basically nothing about teaching others at that time. I was still far to young and dumb. I did my best for those two earnest students, and they claimed I was helping them. I never felt like I did much.
That prof's history classes were EASY for me I could pull A's without much effort because I loved history and his lectures were VERY organized. He wrote out his detailed outline for every lecture at the start of every class for whole class to see, and it tied in very closely with the outline of the textbooks we used. So for word person like me it was easy to spot critical points (ie test questions/answers) and retain them.
I did my best with those 2 students I was tutoring to show how textbook table of contents was an outline, and if you understood the format it was making clear what most if not all of the key points were that you would get tested on. Once you had solid grasp of what data points you'd need to know, you just needed to memorize them. Shuffling through DIY flashcards, I like to use 3x5 index cards, with question on front and answer on back endlessly for hours while watching TV/movie or at jobs when you could (I worked security and cinema mainly in college besides work study, both allowed lot of paid time to shuffle through flashcards with no complaints from boss).
Another thing I am literally the worst person at is learning foreign languages, I tried 2 different languages in college, dropped the second one because even with a native speaker tutor and putting more time in with tutor than in class I couldn't dream of getting a passing grade and though the prof might have given me a pity C grade I didn't want that. I still haven't figured that one out yet, best I can figure I am so tightly an American English word person that I would probably need to spend 5 or 10 times amount of effort of average person to learn a second language and I just have never had the time and energy free to do so. I can pick up what I think of as very basic tourist level (stuff like please, thank you, excuse me, where is the toilet, or where is the airport) about same as someone else by doing sheer repetition to memorize handful of phrases. But forget getting any of the nuances of real fluency or even basic proficiency.
In conclusion to this wall of text, this is starting to sound like you have a student that is interested and motivated! But they have some major barrier, whether that is missing something that seems intuitive to you so you haven't been able to communicate it effectively, or possibly trauma (victim of violent crime or witness to gun suicide, I've known couple of those people), or something like a learning disability.
I would suggest besides going out in celebration of the effort, or journey on the path to proficiency/excellence, I mentioned at the beginning. You take advantage of the resource here on PF and share more information about what has been tried and what has been accomplished.
Also what the goals are, its also possibly that for this specific student, they are making progress, but they are just on the bottom on natural bell curve for aptatude for shooting so their progress is so slow compared to everyone else you've worked with it seems like they are not progressing.
We haven't seen anything on this thread yet on what the goals are specifically and what performance has been achieved ie metrics.
Can they hit a 10" circle at 5 feet? Further? Is it a problem of meeting standards under time pressure?
What types of sights have been tried? Aperture? Red Dots? Lasers?
IF I was having lots of problems with a motivated student one thing I would do is have them work with laser on reactive target like a balloon or clay pigeon taped to big piece of cardboard. Allows target focus and instant feedback. Plus with laser can see whats going on with grip and trigger control live. Ideally video tape it.
If needed I would make a BIG grid of the reactive targets so they got some positive feedback going.
Hope that helps. Pretty sure we all want you to succeed in helping this student.