If the concept itself doesn't exist in a language, good luck with that universal translator.
Well, English copes easily enough by simply assimilating, and if need be, adjusting. There's no need to translate schadenfreude or kindergarden or blunderbuss, let alone learn German or Dutch in order to get the translation, as long as you learn that this new English word has this certain meaning. This counts as "learning English", not as "translating".
The UT automates even that process by inventing words like "troglyte" for the user and letting him slowly catch on.
Do languages undergo revival? It appears that they simply die out one by one, until presumably only one is left (and with something like the UT, perhaps none). Except of course as hobby projects for an insignificant minority; there is always an insignificant minority available for X regardless of the value of X.
Let me guess - you don't live in a region where multiple languages are routinely spoken/heard in daily life? I live in a city of 80,000+ people in the province of Alberta, Canada - not a large city by many peoples' standards, but still the 3rd largest in the province. On any given day I can hear English, Spanish, Mandarin/Cantonese, whatever non-English language is spoken in the Philippines, the dialect of German spoken by the Hutterites, one or two Middle Eastern languages, and there's a large Cree reserve nearby. Oh, and even though Alberta is in the western part of the country, I do hear French on occasion.
Canada has a shameful legacy of deliberately trying to stamp out the First Nations languages by forcing the children into residential schools. They were taken away from their families and forced to assimilate into a culture that was completely alien - and cruelly punished for speaking their own languages. Now that the residential schools have been shut down and the government has been attempting (in fits and starts) to make amends for many decades' worth of attempted cultural genocide, some Native groups are making a deliberate effort to relearn their original languages. Time is of the essence, though, since in many cases there are just a few people left alive and able to teach the younger generations.
A language is more than just what people speak in everyday situations and what may be written down - when a language goes extinct, so does the knowledge that was only passed along via oral traditions. If something was never written down and the language is lost, the knowledge is lost. Forever.
As an anthropologist/historian, I find that tragic.
So yes, languages do undergo revival. It takes considerable work and dedication, but it is possible. I can't believe that the Federation (Starfleet in particular) wouldn't hang on to linguistic knowledge, for the sheer pleasure of having
that knowledge available, never mind the considerable work done by linguists, anthropologists, historians, diplomats, etc.