In Star Trek (the original, that's why I treat it as a title), the universal translator was a cylinder like device. In Star Trek: The Next Generation it was in the communicator, which is part of the uniform. In Who Watches the Watchers, Troi and Riker have subcutaneous communicators implanted so they can communicate without the natives seeing them use technology (this was the only time in the series they used implanted communicators). This does show us that the communicators can be embedded without being observed. Considering the small size of circuitry at this point, that likely includes the translator circuit as well. (Especially since neither Troi or Riker likely spoke the native language.)
I don't have a writer's guide or direct behind the scenes info on Deep Space Nine or Voyager. There was no on-screen reference to embedded translators on screen, though. Supposedly they still used the standard "worn as an insignia" communicators.
In Enterprise it's referenced and shown, in one case, that the communicator work directly with translator -- there's even one scene (forget the episode) where Archer's communicator stops working and to cover for it, he grabs the women he's talking to and kisses her.
From a behind the scenes point of view, the UT is obviously a writer's device to simplify the writing and the story. When they're speaking with aliens where we would not know the language, we don't hear a translation from the communicator for either side of the conversation. By making it part of the uniform, and something that was worn, that put the entire issue of language in the background, as something that didn't have to be dealt with in terms of plot. (Much like the way the language issue was just handwaved in Stargate: SG1.)
While there may be exceptions, I'm pretty sure that in The Next Generation there were no cases of them losing communicators and still communicating with non-Federation speaking aliens (whatever language it is that the Federation uses!). Since I had hopes of writing for TNG, and ended up pitching to the producers at one point (and had to stop when they shut the doors temporarily, then had a situation that kept me from returning for a long time), and had the chance that I might return to pitch again, I watched that series very closely.
I am not sure if they were as picky in DS9 and VOY, but if they weren't, as much as I love in-universe answers, I'd still say it was poetic license if they lost their communicators and still talked with people who would be using a foreign language.
On the other hand, I'd like to see someone cite episodes of any of the 24th century shows (TNG, DS9, VOY) where they didn't have communicators (or some other translator) and were talking with people who should not be expected to be speaking in some form of "Galactic Standard".