Once a question starts getting downvoted, is it doomed?
Nope. That's why we have the lifeboat badge.
This post was inspired by this question.
That post is explicitly off topic. Yet it was gathering good answers. These questions are dangerous because if off topic questions do well here they redefine what the site is about. Such questions need to be doomed or the site is doomed. It's no surprise that it was down voted to -3 because that is required for deletion.
Suppose a new user asks a question, but it isn't clear what the question is asking. Within minutes, it will start attracting down-votes and votes to close.
That's a different close reason. Yes it will start attracting down-votes, votes to close, comments asking for clarification, and answers blindly stabbing in the dark at it's true meaning trying to get lucky.
The main thing the new user should be doing in this situation is rereading their question and trying to understand how it looks to others. If they manage to spot the problem they should edit to make the question clear. The only time this is a problem is if doing so invalidates well received answers. In those cases posting a new clearer question is entirely reasonable. Preferably with a different title.
At that point, is it even worth the poster trying to improve the question? I get the impression that the question is permanently doomed, with no hope of ever getting voted back up to at least zero, or of getting a useful answer. But if that is the case, what is the point of allowing other users to leave requests for clarification?
As questions age they are reviewed less and less. That's what dooms a question. That's why you should read it carefully before you post it. And it's why requests for clarification should inspire edits quickly while it's still attracting votes.
But understand, up voted and off topic is still off topic. So read the sites rules, meta, and existing answers first.
The poster would be better off deleting it, and writing a new version of the question from scratch.
Sometimes that's true. Especially if the question is on the wrong site. Take it to the correct site after deleting it here. That's why one of my canned comments for newbies in that situation reads like this:
Welcome to Software Engineering. We only support good, on-topic questions. Many sites have different rules. Feel free to take your issue to an appropriate site if one exists. Search existing answers first. Edit your question to fit the sites needs. Please don't cross post by failing to delete your question here.
Something you should understand, there is no magical way to avoid getting downvoted and closed. We can give you advice that will give you better odds of doing well. But even following that will lead to you occasionally getting downvoted and closed. I've had to take my lumps here and I've watched our top reps take their lumps. The community here is critical. They aren't shy about it. It's harsh. But it's what puts the polish on the gems you can find here.
So my advice is take your lumps with a smile and keep at it. I think you'll do great.