I've heard of cases like this before - an LOA recipient without a nomination - but it is extremely rare. What puzzles me is this: The Letter of Assurance is not only sent to the candidate, it is also copied/forwarded to the three primary nominating sources, the applicable congressman and both senators. The LOA is basically telling these nominating sources, "If you nominate this candidate, he/she will get an appointment!" This begs the question, "Why wouldn't a nominating source nominate a candidate who is guaranteed of an appointment by the academy itself?"
I think there are two possible explanations how this could happen.
1. The congressman's Service Academy Coordinator is unaware that the candidate has an LOA. They probably received the letter but you can imagine the deluge of correspondence that comes into the office. It simply didn't get noted. It got lost in the shuffle. This is why I always advise a candidate who receives an LOA to send that LOA to the nominating source (even though the LOA already indicates that it has been forwarded) with a concise explanation indicating the significance of receiving an LOA. This insures that the letter gets put into your file. It's a reminder, of sorts.
2. Despite receiving an LOA, that is no guarantee that the candidate is a good interviewee. Maybe the candidate did or said something during their nomination interview that was off-putting; so much so, that the interviewer thought it was disqualifying, despite the fact that the candidate had an LOA in hand.
Let's not forget that the congressman is probably not making the selections. Do you really think a senator or congressman (especially one who is running for reelection) is going through ACT scores and reading recommendations from teachers? No! They have a staff that does that. The person who is probably creating the slate of 10 nominees for each vacancy is the Service Academy Coordinator who is probably assisted by a couple staff members, some of whom are serving internships. The LOA has either fallen through the administrative cracks or the candidate has done/said something that somebody on that staff found particularly distasteful - and, therefore, disqualifying.