Is it important to continue dance over the summer? I don't think it is life or death but I do think it's best if you can continue over the summer! It is great exercise and most dance studios have dance camps or clinics that are jam packed with lots of dance, crafts, movies etc. in one day or over a few or all week, that you don't want to miss!
You can really gain a lot over a summer time and can definitely get ahead if you want too! It is definitely important to keep stretching over the summer as well or your body can lose it's flexibility, if you do not stretch at all.
So if you choose not to take dance lessons over the summer, make sure you find time to stretch and find time to exercise so you will be ready to jump into classes for the fall without having to backtrack!