If you've sent multiple emails as reminders I think I would just let it go. There is really nothing you can (or should) do to make people sign up. A new year will be much different, and I'm sure you have learned tons that will help you in setting boundaries for the new studio year.
I've been where you are, and I know it's not pleasant, so I really feel for you. It's the one thing that drove me to be more professional, though.
I follow a marketing blog which has really helped me stand up, be strong and communicate exactly what I want from my families and my students. In this link
Seth Godin shares what I think a lot of private teachers miss. For me it means forget the families and students that don't want what I offer, look for the ones that value music enough to commit to the program I want to offer, a year around program.
If you can, view this as a learning experience, and take this summer to read up on pedagogy or whatever you think you need at this time, and be really ready for fall, which will be a much different story.