The Admissions Board assigns a score, called variously on this forum WPS (Whole Person Score) and WCS (Whole Candidate Score). As I understand it, if they see something they REALLY like in your application, they send you an LOA. Unless there is a significant change in your application, it will not be reviewed again by the Admissions Board. If you send in updated CFA scores, ACT/SAT scores, etc, the board will not look at your whole package again, rather, someone will adjust the WCS based upon the formula used for assigning points for such things.
I think you would be correct in assuming that if you did not receive an LOA within a few weeks of the Board reviewing your file, you probably cannot expect one.
I caution against even giving any thought to LOA. The Admissions Board is reviewing THOUSANDS of applications. Thousands. Not hundreds, THOUSANDS. In the past, they have reported sending out 100-150 LOA's.
An LOA is not an appointment. It is possible to get an LOA, fail to get a nomination, then not receive an appointment. USNA1985 had this happen to a candidate she advised last year.
Your goal is an appointment. Those who receive LOA's still have much work to do. For those of you involved in applying for a nomination, you have probably figured out by now that applying for an MOC nom is just as much work as applying to USNA......times three.
If you allow yourself to be disappointed because USNA is not sending you an LOA at this stage of the game, you are in for an excrutiatingly long fall, winter and spring. There were candidates last year on this forum with lots of leadership, multiple varsity sports, 34 ACT who failed to receive an appointment. It is a mysterious process, one the Admissions Board holds closely to the chest. There is nothing to be gained in worrying about it.
Focus all your energy, ALL OF IT, into putting together the best package for your application to USNA, whether that means studying harder for the ACT or working harder for the CFA or having one more person review your essay.........because some other candidate is doing all that and more. Then focus equally as diligently on the applications for nominations. The SA's can be very choosy these days. Put your best foot forward and have a plan B.