tropit.....I also don't get the discard thing.
I keep my jar of starter in the fridge and may use it once a month. Sometimes, even less. (And, sometimes I can go a lot longer than a month!)
If it gets "hooch"...the grey water on top, I just stir it back in because that is where a lot of the flavour is. It may look ugly, but it isn't bad unless you see mold. (Which has never happened.)
I use the starter and then feed it, let it rest a couple of hours on the counter, then return it to the fridge so I have more for the next time.
There is a great baker on YouTube that agrees with this method and he has a no-knead sourdough which turns out well and takes almost no effort and a chocolate chip cookie that is really good. His name is Ben Starr.
Watson