You are able to battle Cynthia once a day. However, this is only during the Spring and Summer time. Just wanted to clarify this up for those who would be disappointed if it was only a one time thing.
I'm sure it seems weird to be able to battle her once a day during those two seasons, but there will be different characters coming to visit her each day such as the two Elite Four Members, Caitlin and Shikimi. So even though it doesn't really make sense to battle her once everyday, characters will be there and will be adding on to the storyline as well.
But yes, we will be able to have rematches with Cynthia, which is a great relief for those who are really looking forward to seeing her. :)