Can you appeal a job rejection? Short answer: No. Well, usually not.
Every few weeks or so, I'm contacted by a job candidate who asks me to reconsider our rejection of his or her application. Here's the internal dialogue in my head when this happens, and I can almost guarantee you it's the same for other hiring managers: "Reconsider the decision? But we rejected you for a specific reason, because you weren't a match with what we're looking for. On what basis are you suggesting we reconsider? Oh, no basis. You just want us to change our minds and decided to take a shot at it. Well, on the off chance that some sort of horrible clerical error happened, let me pull out your resume and make sure. Hmmm, let's see... Yes, the decision was right the first time."
Unfortunately, the reality is that you got rejected for a reason. Maybe your qualifications aren't as strong as you thought they were, or maybe they are very strong but other candidates' are stronger. Or maybe you don't have an accurate understanding of what the job is all about, and therefore your opinion of how qualified you are is built on an erroneous foundation. Whatever it is, you have to remember that the hiring manager knows what she's looking for better than you do.
Because of that, appealing a rejection can come across as saying: "Even though all I know of this job is the one-page job description I read--whereas you know the job, the organization, and the culture intimately--I'm going to reject your judgment and tell you that I know better." You don't want to come across that way.
Some rejected candidates even decide to dispense with me entirely, and instead try to contact the head of my organization to complain about the decision. He immediately forwards them to me--because he trusts me to be competent at my job. Going over the hiring manager's head doesn't endear you to anyone. It's not a good strategy.
All that said, there is one very specific situation where it's OK to appeal a job rejection: when you realize that you have left out pertinent information that might have made a difference. For example: You've just been rejected for a job that requires bookkeeping experience. Your resume doesn't show any, but you've volunteered for years as the treasurer for a local nonprofit, where you're responsible for tracking all the finances and training others in using the bookkeeping software. You didn't think to include it on your resume (although you can and should include volunteer experience, by the way), but now you realize that it might have helped your candidacy. In a case like this, you can send a follow-up email explaining this additional experience and ask if it might change anything. Make sure you explain why you didn't mention it originally.
For tips on how not to get rejected in the first place, see more advice here.
Alison Green is chief of staff for a medium-sized nonprofit where she oversees day-to-day management of the staff as well as hiring, firing, and staff development. She is working with the Management Center to coauthor a book on nonprofit management. Her writings have been published in the Washington Post, the New York Times, Maxim, and dozens of other newspapers. She blogs at Ask a Manager.