Honestly, those who did not get an appointment need to first assess why. Ask the USNA admissions officer to be frank and honest. Have him/her tell you specifically what you would need to make the cut if you reapplied. Your congressional district will likely be the same, so the competition will be similar. If your ACT scores were only a point off from getting a spot, for example, then decide if you want to work on that, and reapply if you have the motivation to do it. If you had a 27 ACT, and you will need a 32 to be in good position for a spot, If you have already taken the test 5 times, and it is very unlikely you will move your scores that much, move on. The admissions formulas for the academies are not that complicated, and you should be able to conclude what area you were short in. The admissions people should be able to make it clear if you aren't certain.
If you were a borderline candidate, and you really want USNA, reapply and boost things you can boost. Academies love reapplicants, and you will get a little extra love next time. Also decide why you wanted Naval Academy. If it was because you loved the uniform and think Annapolis is a cool place, thats all good, but reevaluate your long term thought process. If you want to serve as an officer, and be a leader of men and women who share your patriotism and goals, and believe you would enjoy the military lifestyle, consider applying to other academies too, and ROTC. Visit West Point, USAFA, USCGA, and USMMA. Talk to people there. Tremendous places, which lead to tremendous opportunities as an officer, and you may fall in love with those academies. You may end up singing that old Garth Brooks song "unanswered prayers", and be grateful things worked out the way they did. If you really wanted Navy or Marines, the services ROTC scholarship program are so great that I felt a bit sick when my son turned his down to go to West Point. When comparing the ROTC option with the Academies, they both have pros and cons. If I was a kid and had both choices i would go back and forth, and spin my head choosing. Both end in the same commission.
Assess, evaluate and decide. Whatever you choose, commit to it had core. Have a vision quest and make it happen.