Can a business charge me now for something they forgot to charge me weeks or even months ago?

My daycare has a policy that says after 90 days of attending your child is only allowed 10 days of vacation and any other missed days I am responsible for payment as if my child was there. I have no problem with this, however it turns out the day care was overcharging me for months. When it was brought to their attention they said they would issue me a refund. Except, instead they went back and added up all my child's missed days of school and deducted from my refund. I was never charged for the missing days when they actually occurred and now I feel like it is only being done so they don't have to pay me back my full refund.