I am new to this forum. #1 son was turned down for NROTC scholarship. His stats were at the highest level. However, he was was relatively slow to apply. He did a gap year in Taiwan, already accepted to several schools, and applied for AROTC 4yr from Taiwan. He couldn't have submitted his app any sooner. He got it. He is the only out of stater at his big state school who received a scholarship. I got impression that the university's engineering dept wanted him pretty badly.
To make a long story longer, there are many moving parts. Each branch uses ROTC to train its future officers. One of many reasons to offer scholarships is to try and produce a variety of skill sets to meet their future manpower needs. Time also counts. If they can fill the spots in December, you'll be out of luck if your app isn't in until Jan.
Assuming you are completely qualified, you will still be subject to luck of the draw. There could be a huge group of candiates wanting to study exactly what you want to study at the schools you designate, giving you much more competition. I think this may have been what happened first go round with the NROTC. My son designated Ga tech (nothing but Engineers) and Cal Berkely, the most sought after public in the US.
In my son's case, he designated yet another school for AROTC. His academic advisor advised him against ROTC, believing that Chem Eng and ROTC would be too much work. She's right, but he is did it anyway. I assume all Engineering applicants at his school are getting that same advice. Therefore, one would assume that there wouldn't be that many engineers applying there for ROTC scholarships, giving him less competition.
I know this sounds confusing. My best advise is to use this forum to ask questions and be as specific as possible about your situation. Reveal as much as you can about what you really want to study, what kind of schools your looking at, public or private, in or out of state, etc. I think you'll find some excellent advice.