All of our regular subscriptions do auto-renew, meaning that each time you receive all of the boxes you have already paid for, the system will automatically charge you again. This will continue to happen until you cancel your subscription. Cancelling will only prevent future renewals from going through, it will not affect the boxes that you have already paid for.
Our gift subscriptions, however, do not auto-renew! They simply end once your giftee has received all of the boxes that you purchased for them. (Gifts never expire before those boxes have been received.)