When you say ancient you might be thinking of Latin or Greek, but for Arabic the answer is pretty close to "yes." There are huge archives covering a vast stretch of time that remain, not quite "long lost" but definitely untranslated and under-studied. There's currently a project underway to copy and preserve the manuscripts of Timbuktu, for instance. This is being carried in part by, of all people, a group of Catholic monks in Minnesota who specialize in ancient document preservation: http://www.economist.com/news/christmas-specials/21683977-catholic-monks-minnesota-are-helping-save-trove-islamic-treasures

There's also the San'aa manuscript, one of the earliest complete or nearly-complete manuscripts of the Quran. I'm not 100% up to date on the very latest scholarship on this in the past few years but it's my understanding that access to the manuscript has been strictly limited and parts of it, along with the associated documents it was discovered with, remain un-studied or understudied. Sadly I've also been looking for an answer to the question of whether this document is even being preserved safely given the ongoing conflict in Yemen but have yet to find a satisfactory answer.

Then there's the stuff that's not in a museum or university but that we can safely assume is there. Saudi Arabia, for various reasons, doesn't really allow archaeological digs, and especially not at Mecca, Medina, or central Hejaz. There are quite a lot of questions related to early Islamic history that seem like they might very well be answerable if we had access to the archaeological evidence but we just haven't been allowed to do so. Even more disappointing is that, again for various reasons that we don't need to get into is that the Saudi's seem to be wantonly destroying potentially archaeologically valuable sites.

Also it's not quite "sitting around in a museum" but, and I think this was posted by someone here on /r/askhistorians the other day, but I loved this story of a cuneiform specialist who found a new verse of the Epic of Gilgamesh in a market of looted artifacts in Kurdistan: http://news.discovery.com/history/art-history/new-gilgamesh-verse-is-epic-15100.htm

Most of the above discoveries I mentioned probably wouldn't be too exciting to a non-specialist (for example, an inscription with a hijri date one year earlier than the earliest known hijri date inscription would be a really exciting discovery) but a new verse to Gilgamesh? That's awesome! Just goes to show that there's still a lot of stuff out there for specialists and non-specialists alike.

edit: in case you're curious, the earliest Hijri dated inscription: http://www.islamic-awareness.org/History/Islam/Inscriptions/kuficsaud.html, it's still entirely legible and comprehensible to a modern Arabic speaker 1371 years later. Inscriptions and coins are the bread and butter of early Islamic documentary history. This particular one was discovered about 10 years ago.

Basically any source material that appears in large quantities - in archaeological digs on rubbish heaps for example - will be largely unread for decades. No field in the study of history has the resources to deal with an abundance of primary material.

Major collections like the British Museum have back rooms with thousands upon thousands of cuneiform tablets that are as yet unread, untranslated and unpublished. The University of Vienna has a large archive of papyri from Roman Egypt that it simply does not have the manpower to process.

The worst thing is that when experts actually do get around to studying some small part of these archives, it often takes them so long to get a grip on them that no meaningful results are published until either the project is dropped or the scholar retires or dies. Information about archaeological sites, too, is constantly being lost due to scholar mortality. The backlog isn't likely to go away. In some cases the decay and loss of source material progresses faster than its publication.