How do I get people who sign up for a free program to actually attend it?

I work for a non-profit and we offer free day camps to kids in need thanks to various grants I apply for. Since it's free though, we often don't have nearly as many kids show up as who registered. This is a shame because it's a great program, and our team puts a lot of effort into planning and implementing everything. It also means our participant numbers are lower and this could affect our ability to fund the program in the future. I send reminder emails, request a confirmation response that their child will attend, tell them that we have wait lists and want to allow other children to come if they are unable, etc. We have some families I can always count on, but others not so much. We've considered charging a small fee, but we don't usually run programs that require this so it would increase our administrative costs as well as a fee required to run paid programs in our facility, though at this point it might be worth while. Any advice?