Instead of talking about words falling out of use, how about we talk about "cognate replacement" (there's a good search term for you). So, in English, we say to walk and in Italian they say ambulare. These two words have very different histories, so we'd call them different cognates. In English, we have a less commonly used verb to ambulate, which is cognate with Italian ambulare.
Now, let's take two more closely related languages, Italian and French. Italian's word for "to walk" is ambulare, and in French it's marcher. These two language are both descendent from Latin, which used ambulare for "to walk". So at some point, French replaced its word for "to walk" with another, historically unrelated word.
Whether or not this kind of cognate replacement happens at a constant rate is, I think, a rather controversial question in Historical Linguistics. It is at least as controversial as whether or not genetic mutations happen at a constant rate. There is at least one paper which argues that frequent words undergo cognate replacement at a slower rate than other words, namely Frequency of word-use predicts rates of lexical evolution throughout Indo-European history. I haven't read the paper closely myself, but note that 1) It's published in Nature, which has a bad reputation as far as language oriented papers go, and 2) None of the authors are linguists.
As for societal differences, I know of no hard data, but I would suspect that a well regulated literary culture would slow down cognate replacement, and that high rates of language contact/bilingualism would speed it up.