this is probably a stupid question so please show me the error of my ways

I am only brewing kits but am starting to think about yeast's
I must be missing the obvious but sice yeast is a living organism it seems reasonable that if you were to grow some yeast, as it multiplies, you could continue taking off what you needed indefinately. as long as you give it a happy home and food.
since there are lots of yeasts for sale I guess its not that simple - or we would all settle on our required yeasts and culture it ourselves.
so i guess my question is - can you from an initial purchase of yeast continue to culture it? would you want to? will it for some reason deteriorate/mutate/die for some reason?
though there are lots of posts with specifics there is no real idiots guide (which is about my level
