@usastudent101 - I definitely connect. I truly thought I was going to get in last year as well. But yes, reading those waitlist and rejection letters for me was so hard. To read, “We regret to inform you.” or, “We’re sorry…” just made my heart plummet to my chest. And yes, waitlists are very hard to get off of because now, the admission team is looking more closely at your skills. For example, they accept a kid because they’re really good at swimming. But then that kid does not attend because they were accepted by another school that they’d want to go to. The admission team will look at the kids that they have waitlisted, and choose a swimmer to replace them.
To show your interest, immediately reply to all schools and confirm the waiting list [so they know to keep you on it]. In your email, you should send it to your interviewer and cc the admission team to show them that you’re interested.
In my letters last year, I talked about my favorite memory I had during my interview/tour of the school, and why. I also talked about my recent achievements. Lastly, end with why you love the school so much. Perhaps, if you agree, talk about your passion for it, and that if you’re taken off the waitlist, you’ll definitely go.
Be careful about saying that you’ll definitely go to all schools. Say it to the one school you feel passionate about.
Remember: Keep your emails relatively short. No essays or rants, and physical letters are not needed 
In terms of how often you should send them, perhaps once right now. If they reply, you should reply to them. If they don’t, wait a month, or however long you feel fit, and update them on further interest and achievements. Of course, don’t send a letter every day
But if you’re losing hope, don’t:
This year, I’ve been accepted by two schools.
Even if you don’t get in this year, if you’re interested: work hard and grow stronger. Take the mistakes you made in this admission to apply in the next admission process.
But if you don’t want to apply again, that’s reasonable as well. As my first post says: Boarding school isn’t everything.