I don’t remember it, but the fact that coffee was rationed and expensive surely had a lot to do with the practice; it mostly wasn’t done by choice.
Nowadays, coffee is cheap, so we don’t have to make hard choices like that.
I’ll make mine fresh each time, thanks.
This is a pretty common ‘tightwad’ tip – I’ve seen it in a lot of books on frugality. I don’t do it myself, except in extremity (I need a second pot and am running out of coffee). Usually, though, I use a fresh filter and fresh coffee for each pot.
That said, I do use gonzomax’s grandmother’s method for reusing teabags.
You’re aware, I’m sure, that the very first webcam was for just this purpose?
OK, I’m late coming back, to get my smacks for not treating Coffee as the holy beverage it seems to be to some. I guess I like my like my coffee strong, oily and bitter. 
Them once used grounds got some caffeine and coffee goodness left in em.
Y’all are wastrels, sez I.
Actually, that’s the way you’re meant to do it. Foods fried in fresh oil come out pale and underbrowned. New oil needs a bit of old oil mixed into it for proper browning.
Once you get a good whiff of fermented coffee, or moldy grounds, you’ll be averse to repeating the experience, sez I. 