We don't fully understand the meaning of a falcon scholarship. I have to admit I am so disappointed she did not get an appointment, I am almost ready to cry but don't want to do that in front of her.
Quite often here on SAF, the sponsored prep scholarships are referred to as the "golden ticket." For good reason.
One way to think about this is USAFA wants your DD so strongly, and believes in her, they are willing to wait for her, giving her the opportunity and the financial help to buff up whatever area they found lacking.
If she successfully completes prep, remains physically and medically qualified, and gains another nom (usually not a problem), then this time next year, you will be doing the happy dance.
The year away from home develops maturity and independence that will stand her in good stead and give her additional confidence. She will have a set of friends from prep, so she will already know classmates. There are cadets of all ages in the incoming class. Many are prep, multi-year re-applicants; not all are direct admits. No one cares once you are at USAFA.
These prep schools have a long history of success of helping SA applicants get their appointments. Jump on the website for Falcon scholarships and start looking at the schools.
She will not be behind. Take the long view. It is extraordinarily difficult to get into a SA. She now has a near-guaranteed seat.
If your DD wants USAFA above all, they have told her they want her, but she needs to do this one more thing. She is understandably doing a bit of grieving for the door that just closed, but there is now another one, standing wide open, that goes to exactly the same place. Let her think it through with heart and mind.