Hmm... Not sure I agree with that. I think it'll keep for months in the fridge.You can store the slurry for up to a week, maybe two before you’d need to use it with a starter as the yeast cells will deteriorate quite quickly. If you’re brewing back to back it’s really easy to re use part of the yeast cake. Some people rinse the yeast but I personally don’t and just pitch a calculated amount of yeast/trub.
(@MyQul is the person to ask about this stuff - I'm pretty certain that to him, beer is just a by product or supporting act to the headline show of growing more yeast)
Once I've bottled I generally scoop a sample of yeast (sometimes mixed with grain and hop trub!) in a 50ml centrifuge tube and store it in the fridge.
I don't bother with washing it, but once it's settled out the layer of (essentially sterile) beer on top helps preserve it.
(I know some others freeze yeast with glycerine but I haven't tried that.)
Some (or all) of that yeast sample can then be used to build a starter months later. You can also build a starter (using step ups) from the yeast in the bottom of a bottle of your own or shop bought beer.