Interesting question. I know he has been living with the werewolves because that is where he learns of Greyback's desire to bite all the children that he can. I would say that other people beside Snape would possibly be good at making the potion, or perhaps DD has convinced Snape to make him a lasting supply. I would say that there is someone who is helping to not attack people, and or he is going somewhere that is deemed safe for him to transform without there being threat to people.