terminal dialect?

There's something I've been wondering about this year which some of you might
have opinions on:  we know that nearly every language in existence tends to
undergo successive phonetic changes which over the course of just a few hundred
years can transform the language into something remarkably different.  And
apparently no-one really knows why this happens.  My question is, do we know
anything specific about *when* it happens, i.e. whether one particular language,
given the arrangement of this, instabilities of that, and similarities to
the other, is *more likely* to undergo a certain change.  The conlanging motive
behind this question is the possibility of altering a conlang so that, even if
it were actually used over a longish period of time by a large speakership, it
*will not change*, the possibility of a "terminal dialect" of the language, so
to speak.  I've been putting a lot of effort lately into guiding my conlang down
such a path, though I've never really been sure if such an expectation is even
reasonable; certainly you can deliberately use particularly "stable" sounds,
e.g. no "ps-"s, "pn-"s or whatnot, but is it possible to actually make the
entire language phonetically "stable"?  I know Icelandic hasn't changed much for
hundreds and hundreds of years, but I wonder if this isn't due more to
linguistic conservatism and the small number of speakers than anything else...

Josh