CoachM is correct that wrestling is an easy sport to quit. The two things I've found that keep kids in the sport are success and/or a good relationship with the coach & teammates.
Success can be very different for any of the wrestlers. For some, it's making it to state or having a winning record or making varsity or even winning 1 JV match. For others, it's simply the kind of recognition that CoachM explained. Every kid is different, so you need to focus on what it will take to keep each individual kid out. That can be very tough if it's a large group, but fairly easy when it's just a few.
Even without much success on the mat, kids will keep wrestling if they have a good relationship with one of the coaches. If a kid thinks all the coaches are jerks who don't care about him, then they will quit. If a kid gets along well with any of the coaches or at least respects the coach, they will be much more likely to keep at it. A good relationship with teammates is equally as important. Having a good friend who is also wrestling will keep a kid on the team. On the other side, though, having a good friend who quits will drag a kid off the team with him. As a coach, you need to be aware of who your wrestlers are friends with and what their influence is.
It's a challenge all of us face every year, but it is possible.