Once your child has been waitlisted is there any point in applying the following year?
Why not?
Not with the same application, but with one that shows growth. There are a lot of kids who are admitted on their second time round.
And some kids are admitted off the waitlist on their third try 
I almost didn’t apply to Groton the third time. It turned out to be the charm.
Sure. A waitlist is supposed to mean that your child could have been admitted, but there weren’t enough free spots in the class. Every year is different, too. Your child might have been, for example, the 3rd tuba player in the school band. If one of the admitted tuba players decides to drop band, the school may be looking for a tuba player next year.
On the other hand, it depends on how large the waitlist is. If the school does not take any waitlisted students, it bodes ill for spots opening up in that grade in following years. (One exception: some schools purposely admit small 9th grades, and add a significant number of students to the class for 10th grade.)
If your child was waitlisted to one or more of the extremely selective boarding schools, it would make sense to broaden your search the following year, taking a look at other fine schools in which your child would be a competitive applicant.
Welcome back, @Periwinkle! Long time no see. 
If your child is still interested, then definitely. I was wailisted at every school I applied to the first time around, and now I attend Andover. Admission officers see us in more of a positive light because it shows your commitment of interest in the school and they can see how much you changed for the better in your most recent application.
If you have any questions, feel free to PM me!
When re-applying @stargirl3 and @andoverblue21 did you 1) explicitly emphasize these areas of growth – that seems tricky to do without sounding forced (how much does a 13 or 14 year old change 2) did the same person who interviewed you the first time(s) interview you again?
Also can I ask, did you reapply for the same grade? My daughter (waitlisted to her disappointment at your schools) would have been very much on the young side of the grade, so a re-application for 9 v. 10 is something that we’ve received some hints to do and wouldn’t be too awkward for her.
@DevonAultOrBust I was interviewed by different people. I don’t remember if/how I emphasized growth, honestly. I was also on the young side, but I didn’t apply as a repeat.
@DevonAultOrBust Hi! So basically, the things that changed in my application is that I got some achievements in art and that became my strongest EC in a sense. I also think my recommendations were a LOT better because I was closer w my teachers (I was lucky because my teachers were my athletic coaches) I was considering to apply as a repeat 9th but I ultimately chose 10th and I’m so so happy I did. I love the class of 21 and coming in as a transfer student has been such a smooth transition. I had a different interviewer the second time, but I was definitely more releaxed and I felt more real the second time if that makes any sense. Best wishes to you and your daughter!