Most of those turned down prior to late March are those who: (1) did not complete 100% of their packet, followed by (2) those who completed their packet but did not receive a nom and will not be offered NAPS/Foundation and (3) those who completed their packets and received a nom but were not 3Q'ed -- will not be offered NAPS/Foundation or will not be given a waiver for medical reasons. These turndowns typically occur in February and into March.
Those who are remain are 3Q with noms and those who are in the running for NAPS/Foundation. Historically, the overwhelming majority who get good news hear by around March 20. However, as correctly stated above, every year there are candidates who receive appointments up to April 15 and even later (if on the Wait List). That said, as noted, when you're in late March and don't have an appointment in hand, you are much more likely to receive a turndown or Wait List than an appointment -- at least that has been the case for at least the last decade.
On April 15, you will know your status. If you are WL'ed, then and only then do you still have a chance. Whether you come of the WL is almost exclusively driven by yield and most of those folks hear sometime in June. There have been cases of people being offered appointments at the "last minute," but they are quite rare.
To be very clear, it's NOT over until you receive the final news. However, if you are sitting around on March 31 with no news from USNA, be sure to be working very hard on other options. If USNA remains your first choice and comes through, terrific. If not, you have another great plan for your future.