We can never 'fall' again as thoroughly as we did in the past. Too many artifacts; too many documents/cds/books/computers containing the technology to restart a civilization.
Books fall apart (especially those made in recent times). Computers, cds etc all require electricity, which would probably be one of the first things to go, taking with it reams of digital information. Then account for lack of maintenance (except in isolated environments) and within a century or two, it would be very difficult to recover from.
Exactly. Even though we have a many more means of storage today than we did in antiquity, they're brittle in innumerable ways. The only sort of "permanent" storage would be in the form of a hologram (if the media is durable), however without technology to read it, that's still a gamble.
This is why messages for nuclear waste disposal sites are meant to transcend not only modern media, but also modern language.