I guess I have a different view of this. I think you should quit when you start caring what your rating is and using that as your guiding principle when making decisions. The point to a rating is to pair players who are relatively equal in strength. That's it. A 2000 level player isn't a "better" human than a 400. It just means they are better at playing a board game.
It sounds to me like what you really don't like is losing most of your games. And if that's the case, just play people close to your own rating and it will eventually even out where you win about half.
So as the title asks, at what point should someone quit chess because they're no good at it? When they're winning something like 30%-40% of the time? When they go down to something like 800 elo, or struggle to get that high in the first place?
I don't want answers that are just "when you don't enjoy", that's not the question I'm asking. I only want answers that to do with a lack of skill.
Best answer (judged by me) will be gifted a gold membership.
Lack of skill should have nothing to do with when a person "quits" chess. There are many ways to enjoy the game. You can get as much fulfillment by studying the great players of the past as you do playing blitz and bullet and all that silly stuff people love so much these days. Chess is "the other beautiful game." It is an art. You don't have to be Picasso to love art. You don't have to be Ronaldinho to love beautiful soccer. You don't have to be as sublimely gifted as Tal to love beautiful chess. To me, chess is less about "winning" and more about appreciating the beauty and precision of what happens on that board.