Have you ever been fired from a job? I hope most of you never have as it's a somewhat traumatizing experience. I've been let go from one (and asked to leave another), and even though I didn't like the job and wasn't sorry to be gone, I didn't like getting fired.
Awhile back I saw Brent Ozar ask the question on Twitter: "when do you fire a DBA?". There were a number of answers, and he ended up writing a post that summarized some of the reasons as responses. You can read the post, and the various reasons. I think for most of them, I'd disagree if any incident were the first occurrence of the situation. I know people will make mistakes, and if I don't forgive accidents, I'll never have anyone trust me as a manager.
I also don't think you let someone go for ignorance. They might never have had to deal with a situation. I don't think you let them go if they don't dig deep into systems and find problems. It's always possible they haven't gotten to the one item that causes a disaster.
To me there are two certain places where I'd let someone go. The first is willfully taking part in any illegal activity. I don't think an officer of an organization can allow that to take place. The second is more subjective. I would have to let you go when you've repeatedly shown that you're not becoming a better employee and making the same mistakes over and over again.
Failure to learn is not an option.