Yes; as packermatt said, you have to start BCT. To be more specific, you have to take the first oath which is the day after arriving. If you make it to that, and then are medically turned back, your slot is held. (Assuming you become medically qualified and cleared for the next class year). Unfortunately, if you don't make it to to the 2nd day and take the oath, you will start all over. Including the application phase.
Now; to help not sound too gloomy; the hardest part of the application process is medical, CFT, and MAINLY nomination. With the right coordination with your Representative or Senator; they are almost always going to give you the nomination again. Because it was medical, they want to see you at the academy. Now, had you changed your mind about accepting the appointment; didn't go; then changed your mind and re-applied; the MOC might not be very willing. Anyway, you would need to do the application phase again. No, they won't send him to a prep school.