Whether you are writing about failure or one of the other essay options, keep in mind the primary purpose of the essay: the college wants to get to know you better. On a certain level, your essay isn't really about your failure. Rather, it is about your personality and character. In the long run, were you able to handle your failure in a positive way? Colleges that ask for an essay have holistic admissions , so they are looking at the whole applicant, not just SAT scores and grades . By the time they finish reading your essay, the admissions folks should feel that you are the type of person who will succeed in college and make a positive contribution to the campus community. So before you hit the submit button on the Common Application, make sure your essay paints a portrait of you that makes a positive impression. If you blame your failure on others, or if you seem to have learned nothing from your failure, the college may very well decide that you don't have a place in the campus community.
Does not matter what topic you will choose, what is really important: really believe that you will find your audience. The topic that you are going to choose needs to be interesting for you personally, in other case it would be really difficult to gather all facts and general information to make a good paper. You need to ask yourself: will my future work be interesting to read? Has my future essay a perspective to become a reason for discussion? Is it possible to be serious in talking about this theme but not so much serious to put to sleep this one, who will read it? If the answers are yes, you have a good chance to write an outstanding definition essay.