That's the reason for using a probiotic yogurt. They add the relevant bacteria after they finish ruining it :)
The problem with using yogurt from the last batch is that usually there is nothing left when you finally get to making the next batch... :)
Well, we usually just keep at least one teacup of yogurt to avoid the situation where none has left as you have mentioned be able to make more :D
You just need good bacteria to start with, called the "culture", for your next preparations you can just get a sample from your previous yogurt.
The yogurt you get from stores with preservatives and ultra long shelf time, a.k.a. all bacteria is cleaned up to prevent it going sour, wont work, find someone that has real yogurt.