I'm gonna tackle this from a weird angle, but bear with me. My short answer: lots and lots.

Honestly, I'd say this is a better question for an archivist than a historian. Historians know that much of the past isn't even recorded at all, sure. And they know that quite a bit of what is recorded gets lost, if anyone attempts to preserve it in the first place. But we also like to adopt a kind of "save everything" mentality when in practice that doesn't work. It hasn't for decades (if it ever did). Archivists, in contrast, constantly work on better ways to discern what about the past ought to be preserved (not to mention can be preserved. Budgets and time are limited).

Ignoring the vast amounts of information which never get recorded (did you record all your thoughts today?), even what is recorded is far too much to save. Think about all the "paper" (electronic or not) generated by the US government every day. You think it all gets filed away somewhere neatly? We'll be lucky if 5% of it gets saved beyond a few years.

And how does one choose what makes the cut? Archivists and historians used to approach that question similar to how this question is phrased: by assuming there are certain specific events/people/ideas that are worthy of preservation, and focusing on those. It led to incredibly biased records that privileged one viewpoint or entity over another (such as preserving the policies and records of a colonial government and ignoring records of the colonized). This approach was based on highly deterministic theories of history that have since been debunked.

Historical research has since been expanded to include many more perspective and indeed cautions strongly against trying to privilege one perspective over another. Whatever else it's done, this switch has made the job of an archivist incredibly difficult because the types of questions historians ask have not only changed but become much less predictable. It's impossible to predict with certainty what researchers will want to know in 50 years, so how does an archivist prepare for that?

In short, they stopped really trying a few decades ago. Where they once aligned, the archival and historical professions have largely diverged since the mid-20th century. In a sentence, archivists today focus much more on using records to comprehensively describe the structure and function of a person or organization's existence rather than try to fully interpret or anticipate significance. They don't concern themselves with what's going to fill the history books because there's no longer any conceivable way to anticipate it.

Okay, so how is this rambling answering your question? It's to try and illustrate to you that it's impossible to try and quantify what exactly about the past has been "lost" beyond simply knowing it's a lot. Much of it never gets recorded, much of the record doesn't get saved, and the means by which archivists collect and preserve the past represents a rational response to an undeniable reality: that history is a moving target. It's not a task with a progress bar. The remnants of the past are not pieces to a jigsaw puzzle, where we can complain that we don't have all the pieces. History is rather a means of collective reflection on where some or all of us stand, and how we got here.

Edit: Oh, for a fantastic book on how the history and archival professions have interacted and diverged, see Blouin and Rosenberg's Processing the Past. Hell, it describes the individual development of each profession very well.

Most of written knowledge for a given year for most of history has been lost. ~700 years ago Ibn Khaldun lamented this: "There are many sciences. There have been numerous sages among the nations of mankind. The knowledge that has not come down to us is larger than the knowledge that has. Where are the sciences of the Persians that 'Umar ordered wiped out at the time of the conquest! Where are the sciences of the Chaldaeans, the Syrians, and the Babylonians, and the scholarly products and results that were theirs! Where are the sciences of the Copts, their predecessors! The sciences of only one nation, the Greek, have come down to us." (Muqaddimah 8, trans. Franz Rosenthal)
Fortunately we have recovered some of those peoples' texts, more than what was available to Ibn Khaldun.

The evidence for this is the numerous authors from earlier periods who we only know of because their name is mentioned or a line of their work is quoted by another author. Their works are lost, as are the writings of authors not even mentioned in the texts of others. Even of well attested writers often only parts of their work survived. For example of Polybius' Histories only the first 5 of his 40 volumes exist fully intact.

Edit: I haven't seen exact estimates on percentages of survival before but here's some stats to give you some idea. "...of the 772 Latin authors whom we know by name 276 are merely names, 352 are known only through fragments of the remaining 144 (around 20% of the total) we have one or more works but rarely their complete output." (Micahel Lapidge, "The Anglo Saxon Library" 131) Among other caveats, keep in mind that's only for one language, and for a language that was widely spoken for over a millennia which helped ensure works in it survived.