I'm not sure there's a lot of good reference material for when people should give up. Normally, I wouldn't try and help – it's not like I know anything, and these are some high stakes decisions. Should someone give up on their dream? Who am I to even suggest that kind of thing?
But I think a reasonable heuristic is: give up on tactics almost immediately, once you suspect they won't work, but if you have a dream, an abstract dream – keep trying a little longer. Try differently, if your approach isn't working. Try harder, maybe – but maybe try less hard. If you aren't getting results, you probably shouldn't put all your eggs in that basket.
I think people re-start their progress towards goals much less than they ought to. We get trapped in one angle of attack, and that's the only method we use to chase our goals. Sometimes people confuse the mechanism with the outcome. They have such specific requirements for success they couldn't possibly hope to really succeed. Any tiny change to their plan, a change almost no one but them would even be able to notice, would feel as though they've abandoned their goal. Well, that seems pretty selfish to me.
I don't mean that as a harsh condemnation, just as a banal remark that your goals should have something to do with how you relate to other people. If other people can't notice a change, and the abstract point of the goal is achieved, that's better than most people get. So why complain? I think some people use goals as a way of self-indulging, imagining things so specifically it relieves them of the obligation to actually do anything. If things go slightly off-plan, they obviously should just abandon ship – it's all or nothing for the hyper-specific fantasy result of their goal, so why not give up after the most minor of speed-bumps?
This is all by way of saying: I'm modifying my approach here on the blog. Daily publication imposes absurd costs to long-form writing, and doesn't produce a lot of work I'm truly proud of. The involuntary torrent of ideas is good, but there aren't as many connections between ideas, and I think that's important too. I'm getting better at writing, but slowly, and I'd prefer to write things I can't just describe in conversation – something worth recommending people read because I've taken the time to make sure a complex idea is communicated clearly.
My current goal is posting once a week – starting today, that would put posts on Sundays. I have a couple ideas for posts, but I'd like to see how the writing process pans out for those ideas – I'd like to avoid word-count goals, but I'd also like to only publish more substantial things. I'd also like to spend more time explaining the context behind ideas, instead of encouraging people to research things themselves. I've yet to find someone comfortable with actually doing that, as good a habit as it may be. But this should contribute towards the goal of making self-contained recommendable... things. I'm not sure I'll change the focus on the content here, so it'll still be hard to describe. Hopefully that part of this plan isn't the one that's keeping my Google Analytics at ~0 visitors.