Quitters never win. Never quit. Never give up. Et cetera.
I don't always agree with those sentiments. It IS okay to quit, provided you do so for healthy reasons. Giving up and losing under the right conditions is A-OK and you shouldn't be ashamed of doing so. I went over this a bit in this post but this is more specific. It's also mostly in the context of competitive gaming. And specifically, about quitting long-term, not moment-to-moment acts of willpower.
When and why is it okay to quit? Well, one thing I've believed in for a long time is this: you must know what the rules before you can break them. Cartoons and drawings might not be done with a realistic style, but they're typically based in realism and an understanding of anatomy, of light and shadow, of perspective and proportion; somebody who doesn't understand those rules shouldn't be breaking them. When you do break them, you should know exactly why, and what effect it will generate. Not knowing them at all, however, is inexcusable if you're going to take your art seriously.
Likewise, you shouldn't quit unless you understand exactly why you're doing it, and it's done for the right reasons. Only break the rules if you understand them.
Rule one: you should never have a quitting habit.
Looking for excuses to stop doing hard or difficult work is a thought habit, and it's a crappy one. Mastery and success are rarely achieved by going, "wow this is kind of hard, I'm going to go watch cartoons instead."
What are the signs of a quitting habit? When something gets difficult, you look for other stuff to do. You can always find convenient reasons why it's absolutely fine for you to be stopping. You ask "am I really expected to do this?" with any degree of frequency. When you constantly try to positively confirm that quitting is okay, that you should be allowed to in this case, that it's totally fine... in those cases, it's probably not.
The quitting habit is rooted in pain avoidance, and the desire to eliminate discomfort. But growth is done by doing things beyond your ordinary capabilities until those things become comfortable. Growth happens in failure and pain and sometimes even regret. If you have a quitting habit, one of your first priorities should be identifying it and eliminating it.
Rule Two: you should establish your goals and keep them in mind when you think about quitting.
I've mentioned that being goal-oriented and results-oriented can be detrimental, because it can make you sacrifice good habits for short-term results. It can encourage negative self-talk, when your goal seems so far away. It can make you neurotic, always asking "am I moving closer to my goal? Is this improving me, right now?! Rargarargabargle!"
But when you want to quit, and you start thinking things like, "well, I didn't really want it anyway..." your established goal becomes your guiding light. You think, "yes, I did want it. I still want it. I want to be skilled and amazing at this thing, and I want to improve, and I can't do that if I quit. It's okay if I try my hardest and fail, but it's not okay for me to quit now." You have to remind yourself that your original desire outweighs your current desire, the one that wants to avoid your current discomfort, or fear, or pain, the one that's afraid of looking dumb and weird in front of strangers when you screw up.
Rule Three: Quitting to avoid certain problems might be a sign you should be fixing the problems, not quitting.
Should you quit playing a game if the game always makes you angry? Or should you investigate the source of the anger? If you don't want to look bad when you lose, maybe you should focus on your fear of failure, rather than avoid things you can lose at. It's likely that if you've got a common problem with various things you do, it's probably not because you haven't found the right endeavor. It's probably because there's another underlying problem that you're ignoring by switching tasks.
Rule Four: Not quitting can be a bad habit, just as bad as quitting.
We're getting into the gray areas now. Our real goal should be avoiding neurotic behavior. I'm using the definition by Karen Horney, which says "In essence, neurosis is a distorted way of looking at the world and at oneself, determined by compulsive needs rather than by a genuine interest in the world as it is" (thanks Wikipedia).
If you never quit anything, even when it would be extremely intelligent and helpful to do so, because you're paranoid about being labeled a quitter and you are compelled to never leave anything unfinished... that's just as bad as quitting everything you do. It means you're bad at changing your mind when the situation demands it. It means you're obsessive and will over-invest resources into pointless endeavors at the expense of other endeavors. This isn't okay, and this is exactly why quitting is sometimes okay.
Quitting. Stopping. Retiring. Persevering. Your reasons for doing these things matter. You want your emotions and decisions to serve your goals and purposes. Willpower and discipline help this; neurotic behaviors and poor habits do not. When quitting is a pain-avoidance tactic, it will not serve you; when you refuse to quit because you can't bear to abandon something under any circumstances, then you are not being served either.
Rule Five: Follow your current goals, not your old ones.
I don't mean "obey your immediate impulse." Your immediate impulse is going to be something like, "my feet hurt can I sit down," or "Jesus that lineman is huge I'm going to hide in the locker room now." I mean that you should check up on your objectives every now and then to see if they've changed. You shouldn't be so attached to old reasons that they distract you from current goals.
This is where self-honesty comes into play. Don't lie to yourself. You might be using a current short-term goal to avoid pursuing an old one. Obviously that's bad. But maybe your short-term goal is so important you should be abandoning an old one. So obviously you don't want to be blind and stubborn.
When does it stop though? You can argue back and forth, "I don't love this game anymore and it's okay to stop doing it," followed by "I shouldn't have a habit of quitting just because I'm a bit unhappy at this exact moment." Without a good quantitative way to measure which decision is better, you could be at this all day. So really, I guess it doesn't end until you decide. You have to live with the uncertainty until you've burned one of the bridges and crossed the other. Make the best decision you can, and make it in your own best interests. Don't lie to yourself about why you're doing it. Take your own health and happiness into account, and don't make these decisions impulsively. Then learn from them if you can, should they not work out the way you want.
In summary? Quit when quitting will help you meet your current and important life-goals. Don't allow frustration and temporary pain to make you abandon that which is matters to you. It's that simple, and that difficult. Try to keep the above rules in mind. I hope they help.
Thanks for reading.