We have lost huge proportions of ancient writings because of the amount of resources making and maintaining enough copies took, and the resulting physical destruction.
A lot of works that we know had a big impact on culture, for example, are only known through us through quoted fragments in the works of others. Heraclitus "On Nature" (though even the title is not certain) is one example - a work significant enough that over a hundred fragments were preserved through quotations in the work of others significant enough for their works to have survived, but still the fragments makes up only a tiny portion of his work.
And for every significant work we have fragments of, or know of, there are bound to be huge numbers of works we don't know of because they were only ever mentioned in other works we have lost.
We may have become better at protecting paper copies, but they still require someone to carefully maintain the archives and ensure new copies are made once, inevitably, the number of copies of the works will dwindle with damage.
Having it on paper does not remove the need of an archivist; and the sheer volume required for paper copies means that even with a tiny number of locations suffering environmental damage every year, over time the number of copies will dwindle and new copies will need to be made.
This is true of digital copies as well, but the ease of making them and the density makes it increasingly possible to store larger number of copies, and re-copy them regularly. The biggest hindrance today, I think, is curating the increased volume of material published only, more than the challenge of ensuring there are enough copies.
> So if you have an archive on 5 1/4 inch floppies from, say, thirty years ago and a printed copy I think that the printed copy is likely to be the only one that is now readable.
The amount of archived productions of material for home computers from further back than that suggests that while if there is only a single archive extant, chances are you might be right, it doesn't take many copies before the odds of successful complete retrieval are quite good.
Sure, there is a risk there will be a gap in which we lose material that was only published on more perishable material, but that would by no means be the first time that has happened either - what survives to date is largely the subset that was important enough to be made available in the most durable means and then copied and re-copied because people at the time found them important; not by any means everything.