I have two successful tech IPOs and counsel CEOs on topics just like this. Here's my answer:
It depends on what they are failing at. If they fail at a project (substitute "company" if that makes more sense to you) that has a very high chance of success, then that's a red flag. But, if they fail at a project with a low chance of success -but, they embarked on it because if it was successful the rewards would be big - then no big deal.
I know it's difficult to calculate but you should always try to do an analysis like this:
Project A: 30% chance of success but $10 million return if successful yields an expected value of $3 million.
Project B: 80% chance of success but $3 million return if successful yields an expected value of $2.4 million.
The other half of the answer is, how did they fail? Did they fail because of outside factors that they didn't recognize or plan for? Did they fail because of lousy execution? Did they fail because they hired the wrong people? DId they fail because they misjudged the market?
Lastly, optimism bias has us believe we are better than we are and that we control our own destinies. WRONG. Outside forces play a much bigger role than we think. We've all taken on assignments that we thought we could knock out in a day or two but actually took a week.
The other thing about optimism bias is that we hold on too long and won't admit defeat. We all know people who fail to kill a project and throw good money after bad. When we think we're going to lose then we tend to do risky things. (There is a reason the betting on long-shots goes way up at the race track as the night goes on - people are willing to take on more risk in an attempt to avoid losing.)