Namely, the increasing likelihood of data becoming forever lost - entombed beyond hope of rescue in the very media intended to preserve it.
"Increasing likelihood" is a dubious claim, for a number of reasons.
You haven't presented any statistics on how likely a given datum (or any other data unit of your choice) is to be lost today. We're producing, and more importantly copying, information at a tremendous rate today; certainly there's a vast amount of what would have been ephemera in any other era which is being preserved for unprecedentedly long times, and is unprecedentedly easy to retrieve. Take, say, all of Twitter (please).
The article says nothing about data-loss rates over the historical period it covers, aside from generalizations about backups and the like. Nor do you. So we don't even have any evidence at hand to claim that in the computer era the likelihood of information loss is increasing.
For that matter, how is such likelihood defined? Ratio of bits lost to bits preserved, or to total number of bits generated? That's clearly methodologically unsound; we know there are many bits we don't want to preserve, so they can't be considered "lost" in any meaningful sense. Number of occasions when data retrieval fails? That's hard to normalize for historical comparison and also doesn't assign value properly to different data collections, and it doesn't account for losses we'll only discover in the future. Cost of data loss? Even if we attempt to normalize that (accounting for inflation), we run into all sorts of difficulties with historical comparisons because the relative value of information is highly context-dependent.
We don't have any way of measuring how much information has been lost from previous eras, generally speaking, because it's lost. How much of the written output of, say, Periclean Athens are we missing? We know about some of it because of references in works that are extant, but that tells us very little about what else might exist.
Every time the Reg publishes a story on storage technologies, someone raises this topic - as if it weren't widely discussed in academia and industry, as if there weren't all sorts of proposals and standards offered to address it, as if there wasn't an industry segment that exists just to address it. Yes, data loss is an important issue, and it's one that everyone who uses information technology for anything not trivial (which includes most normally-competent adults in the developed world) should be aware of. But it's not well-served by postlapsarian grumbling about the frenetic pace of modern technology, sympathetic though I might be toward that sort of GOML sentiment.