Economist David Clingingsmith has a 2013 paper on this topic (pdf). It seems that languages are stable at a lower margin of speaking community than I would have expected:
Scholars have long conjectured that the return to knowing a language increases with the number of speakers. Recent work argues that long-run economic and political integration accentuate this advantage, leading larger languages to increase their population share. I show that, to the contrary, language size and growth are uncorrelated for languages with ≥ 35,000 speakers. I incorporate this finding into an evolutionary model of language population dynamics. The model’s steady-state follows a power law and precisely fits the size distribution of the 1,900 languages with ≥35,000 speakers. Simulations suggest the extinction of 40% of languages with < 35,000 speakers within 100 years.
You will find other interesting papers by Clingingsmith here.