So I had to reword the question from "how long does it take to sharpen a knife" to something more answerable, but I am afraid the answer will still be disappointing for you.
- It takes as long as it takes - we cannot give you a length of time after which it should be ready. You have to recognize by yourself if the knife is ready or not.
- The ability to tell whether your bad results are caused by not spending enough time, or by something else, comes somewhat slower than the ability to sharpen a knife properly. So you cannot use "time spent" to control your learning process.
I hope that the reactions you saw to the question (including my own answer) will not discourage you. It is great that 1) you are picking up a new skill, and 2) trying to actively troubleshoot it by making a hypothesis about what is going wrong, and then acquiring more information about whether this could be the right reason, and 3) looking for that information somewhere (for example here on the site) instead of trying to figure everything out by yourself. I will try to explain why it is so difficult, so at least you can better what you are facing, even though I can't offer you a viable solution.
Sharpening a knife is a skill. It is not learned in the sense we learn stuff in school using declarative memory ("Charles the Great lived in the 7th century CE"), it is learned by training. And unlike a skill which requires you to only interact with information (such as being able to multiply two numbers) it is a skill that requires you to interact with physical objects, and because of that, anything you can learn from information-only channels such as websites will only be of limited information.
The best way to learn how to sharpen a knife is to observe how somebody sharpens it, and then try to repeat it - basically, apprenticeship. The second best is if you only try by yourself, but have somebody who can evaluate your results, and recognize what you are doing wrong. You chose a third way - read the theory, then try it for yourself. This is a viable way of learning, but it is very time consuming, especially at the beginning, when you get almost no successful attempts. (And in my experience, knife sharpening is a skill with an especially high rate of botched early attempts). And while you are so early in the process, you don't know what is the right way to do it. Then will come the phase in which you have some successful attempts and some unsuccessful ones, but you will not have yet built the experience of what causes your good attempts to be good and the bad ones to be bad. And only later will you be able to recognize this, but that comes after you have a great rate of good attempts. So don't expect to be able to correct yourself at tbe beginning, trial and error involves a big deal of random variation and boneheaded persistence.
To address your exact troubleshooting idea again - you are quite right that there are times which are way too short for sharpening. Even the best world expert will not be able to sharpen a blunt knife with two strokes, nor be able to do the necessary number of strokes in two seconds. But this just means that there is some lower limit for the time necessary. Where this limit lies exactly (and exactness is actually impossible here, because there are tons of factors we are not holding constant) is rather immaterial for your case, because at the beginning, you will be doing many more wrong strokes than right strokes, so your first successful attempt (and "success" is also not a binary thing here!) will take a lot longer than the theoretically possible limit. So you should be going at it for a long time at first, and the shortest possible time doesn't affect what your shortest time you should train per knife. At the other end, it does not help you decide on the longest time per knife either - to oversimplify it, if you are doing 100 wrong strokes per 100 right ones, you will never get ready and should stop, but if you are doing 99 wrong strokes per 100 right ones, you will get a successs eventually (taking you about 100 times longer than it would take an expert stroking at your rate) and should continue. And since you cannot recognize if you are doing wrong or right strokes, you cannot recognize if you are caught in the endless situation or in the slow-advance situation.
Summary: forget thinking about time. Just invest all the effort this kind of training requires, or take the working shortcut of working with an experienced trainer.
