There are two reasons you might give up: the project or the people.<p>Most projects have some good idea buried within them. Often instead of giving up you can figure out what the good idea is, and refocus on that. But there are cases where you should give up on an idea: for example, when some external change has made it obsolete.<p>It's harder to say when to give up on the people. Probably some people are not meant to be startup founders-- either because they lack energy, or because they're hopelessly impractical, or because their minds are more suited to other work. It's hard to judge this for oneself. Sometimes it's even hard for me as a neutral observer with a lot of practice to judge.<p>In practice most dying startups get garbage-collected by money constraints. If you can't convince customers or investors to give you money, eventually you have to give up and get a job. It may be that test is the best we can hope for.
I wrote a blog post ( <a href="http://illicittech.blogspot.com/2007/05/sunk-cost-fallacy-and-dilemma.html" rel="nofollow">http://illicittech.blogspot.com/2007/05/sunk-cost-fallacy-and-dilemma.html</a> ) about this, but basically, people are irrationally attached to things they've invested in. If it's (objectively) not working, put it aside and try something else.
This is a very important question, and I'm glad to see it discussed. Any idiot can run something into the ground, but the tricky thing is to know when to give up and try something new. Do it too soon, and maybe you didn't really do all you could. Too late, and you look "bull-headed", rather than the more flattering label "persistent" that gets applied to successful startups.
Get out when:<p>- you have no more passion (go find a more interesting project)
- you run out of money (go work for a few months and save up some seed capital, and find a more interesting project)
- you become seriously unbalanced (emotionally, spiritually) for prolonged period of time (say, 1year).
- you have serious health problems
After 2 years, if growth is linear instead of exponential and you haven't figured out a business model not exacty where this product is going. Basically. :).