I've read Ostler's book (several years ago) and I don't think he's quite as deterministic as Legolas's post makes it seem.

Having said that, Hebrew died out as a spoken language around the time of the Babylonian captivity. After that, everyone in the region would have spoken Aramaic (including, famously, Jesus). Hebrew was retained solely as a liturgical language, the way that Latin was used in the Catholic Church before Vatican II. Aramaic continued to be used well into the diaspora period, as becomes evident from the fact that the Talmud, Zohar and many other religious texts from the late Classical and Medieval periods (particularly in Spain) are written in Aramaic. Hebrew was consciously and artificially resurrected as a living language as part of the Zionist movement. As a result, the fact that Aramaic is pretty much dead (the last communities that spoke it have been disrupted by the Syrian Civil War) but Hebrew is alive is very odd indeed.