I don't think 12 months a year would be beneficial to kids. I think actually teaching children while they attend school and making an education a priority is more important.
Perhaps Brian Leekley is on to something. Making the semesters shorter could be a good idea. Instead of just two painfully long semesters that most schools use, perhaps dividing up the school year into 3 or 4 sections would be best. I am still all for giving kids some type of summer break, but perhaps not as long. A month might be enough.
I remember being in school and hating it because the end of August or beginning of September meant being stuck in school until June of next year with pretty much the same boring old subjects. Perhaps a better strategy to keep children wanting to learn would be breaking the school year up.
After a few months, kids get to pick some different optional subjects they would like to take the next few months. Sure, English and Reading and Math and all that type of thing would still be required, but other optional subjects could change... like 3 months of Earth Science, but then 3 months of Biology, and after 3 months of French, then the child could choose, "Do I want to stay with French the next months or switch to Spanish?" Making school interesting for children of all ages would probably help a lot.