Many startups go through a point a few months before they die where although they have a significant amount of money in the bank, they're also losing a lot each month, and revenue growth is either nonexistent or mediocre. The company has, say, 6 months of runway. Or to put it more brutally, 6 months before they're out of business. They expect to avoid that by raising more from investors. 
That last sentence is the fatal one.
There may be nothing founders are so prone to delude themselves about as how interested investors will be in giving them additional funding. It's hard to convince investors the first time too, but founders expect that. What bites them the second time is a confluence of three forces: 1. The company is spending more now than it did the first time it raised money.
2. Investors have much higher standards for companies that have already raised money.
3. The company is now starting to read as a failure. The first time it raised money, it was neither a success nor a failure; it was too early to ask. Now it's possible to ask that question, and the default answer is failure, because that is at this point the default outcome.
I'm going to call the situation I described in the first paragraph "the fatal pinch." I try to resist coining phrases, but making up a name for this situation may snap founders into realizing when they're in it.
One of the things that makes the fatal pinch so dangerous is that it's self-reinforcing. Founders overestimate their chances of raising more money, and so are slack about reaching profitability, which further decreases their chances of raising money.
Now that you know about the fatal pinch, what do you do about it? Obviously the best thing to do is avoid it. Y Combinator tells founders who raise money to act as if it's the last they'll ever get. Because the self-reinforcing nature of this situation works the other way too: the less you need further investment, the easier it is to get.