There are some who will say "never give up." I would agree that if you really want to be a successful author, you must never give up on the process of trying to get there. But what about your stories? What if you have a story that's not coming together? When it's not working, how do you know whether to try to fix it or to let it be?
Here is my first piece of advice. If you don't care about the story, then you can give up.
But wait. What about "never give up"?
Only give up on your story if you don't care about any of it. At all. And the important point of this post is that it's going to be pretty rare that you don't care about anything in a story you've been working on. Don't look at a story like a single block, but as pieces coming together. Break up your concept for a minute and take a look at what it's made of; then ask, "Which parts of it do I really care about?"
Here are some possible story elements that may be worth keeping:
Maybe you want to tell a story that will bring up issues surrounding environmental protection, or about the loss of a parent, or about ethics in medicine. If that issue deeply speaks to you, hold onto it.
Maybe you think your main character is so amazing and you dream about her, or it feels like he speaks to you, etc. Maybe the elements of that person's personality just won't leave you alone. You may find that you have to change everything around him, or that you have the wrong main character and you have to promote that other character - the one you care about - into the limelight.
Is it the city you've always imagined? Or the steppes? Is it the social aspects of the society you've created or the magic system you're working with that really gets you going? Don't toss a whole world away if it moves you.
This happens, and that leads to this happening, but then that other thing happens, and guess what they have to do? You may have particular sequences of events in the story, or particular single events that must occur - and they must occur, because they're so exciting that you just can't bear to let them go. So hang onto them.
You know, that one scene where the two people are doing that thing together and this happens and they realize that and it changes everything? Well, there can be more than one way to lead into a situation, and the scene itself may be able to stick around even if aspects of the characters' attitudes change.
The feel of the text is right where you want it, but for some reason the events and the characters aren't coming together, or the world feels like it has holes in it. Keep the draft so you can keep the evidence of the words you used to create that fabulous tone.
Now we get to the part where I talk about starting over. In a way, a story is a bit like a musical chord: all the different elements have to come together and resonate just the right way. Sometimes you're working on a story and something about it isn't working, but you can pinpoint the particular issue (say, the psychology of one of the characters) that you need to fix. Then you can go in and try to fix it. But say the whole thing is strangely off, and it feels like multiple elements aren't matching up, and they're creating dissonance. At that point it might be a good idea to start with a blank file.
Notice, I say "start with a blank file," not "start over." Starting over is a horrifying idea because it makes us feel like none of the words we've written, none of the effort we've put in, has been worth anything. But even if we've only got one element that will be retained, it's still worth that time and effort. And most of the time you'll find that you'll have 50% or more of the original concept remaining. The best reason for starting with a blank file is to keep the old text from pulling you back into the old chord, and the old broken harmonies. If you can redo the concept in your head, and start with a blank file, you may find that all the stuff you really care about will pour out of you in just the right way.
I had a story that I'd written half of, but which felt like it was never going to be finished. I had a character, but her motivations seemed all wrong. The theme of the story was belonging, but the belonging idea was totally implausible because the plot of the story called for too short a timeline for any kind of plausible belonging to kick in. So I re-tooled the character, changed the theme, brought in a different backstory, and changed only just a little of the front story, and suddenly everything started coming together in my head. I pulled up my blank file and it started getting written, flowing in a way it hadn't before. I've taken big pieces of the old text out of the file where I kept them for reference, but a lot of the stuff that had made it feel clunky was no longer necessary. With the story's new configuration, it was clear where the excess lay and how to remove it.
As long as you have something in your story that you believe in, don't chuck it out entirely. Keep what has value, even if you have to shelve it and think about it for a long time. The things on your shelf may come together differently and let you start over. And when you're starting over because it feels right, and you're excited about the way it feels now... it doesn't really feel like you're having to start over. It feels like an opportunity.
It's something to think about.