When things are often repeated across generations, they can:
a) always be true (we generally go to lower standards from the viewpoint of the previous generation, or even from an absolute viewpoint).
b) always be false
c) Sometimes be true and sometimes be false.
I'm not sure why people immediately jump to (b). Perhaps it's comforting to dismiss any worry of decline, and to always attribute it to change. Or it's not fashionable these days to even think about decline (it marks one as old and not "going with the times").
I find (c) much more plausible. After all, whether Socrates said this or not, some such decline happened after Socrates (the dissolution of the Athenian state and its eventual collapse) -- and several other times (in later Rome, etc).
And conversely, for huge periods of time people have not had much to complain regarding their children having some different lifetimes, because unlike ancient Athens or Rome or the US 50s and 60s or so, nothing much changed between generations -- a rural family in most of the world would have the exact same day in day out things to do, the same customs, etc, for centuries, with the very subtle and slow occasional imported innovation.
It's also funny those that while many would say that steady cultural decline couldn't possibly be happening, as many as all convinced for steady cultural progress -- like history is like some kind of march towards more and more enlightenment. Of course those people have never read history, or experienced how a steady and advanced country (or world, in 1939) can turn backwards in a moment's notice.