An assumed attribute of expert physicists is that they learn readily from their own mistakes. Experts are unlikely to make the same mistakes when asked to solve a problem a second time, especially if they have had access to a correct solution. Here, we discuss a case study in which fourteen advanced undergraduate physics students taking an honors-level quantum mechanics course were given the same four problems in both a midterm and final exam. The solutions to the midterm problems were provided to students. The performance on the final exam shows that while some advanced students performed equally well or improved compared to their performance on the midterm exam on the questions administered a second time, a comparable number performed less well on the final exam than on the midterm exam. The wide distribution of students' performance on problems administered a second time suggests that most advanced students do not automatically exploit their mistakes as an opportunity for learning, and for repairing, extending, and organizing their knowledge structure. Interviews with a subset of students revealed attitudes towards problem-solving and gave insight into their approach to learning.