You could do that, but after some time yeast will start to mutate. I don't know how long that is, but you certainly can't keep it going indefinately like you can sourdough.
IMHO, the best way to save on yeast is to wash the trub from a batch. You can easily get 4 batches out of the first generation, then 4 more from each in the second generation. That's 16 plus the original, so seventeen batches out of one vial of yeast. Plus, the yeast will store well in the fridge, so you don't have to brew the same style over and over again.