The maintenance of a single cultural tradition across much of three continents over a million years by exclusively social transmission seems incredible. Some have suggested that the handaxe is hardwired into the human genome, a proposition that seems even less credible (at least, to me). Absent these means of transmission, we are left with the proposition that the handaxe did not fade from the earth because of its functional utility -- either it was the tool that did the job the best, or it was the best tool that humans were capable of making that did the job adequately. If function and human ability combined to make it so persistent, it should not be the least bit surprising that the form should recur in later contexts -- in the scenario of recurrent invention, it never really went away. The production of handaxes on large Levallois flakes seems especially relevant.
I'm probably not as pessimistic about the possibility of purely cultural transmission of the style over such a long period -- culture seems to me to be fairly conservative in retaining selectively advantageous variation when interaction is low -- but it also makes sense that there's some pretty strong functional selection operating on a form that allows such a pretty low amount of variation over that amount of time. There doesn't seem to be that much stylistic license allowed in the basic design (is is a pretty simple technology, after all) so it's tough to tell what part of the variation is determined by selection and what by cultural interaction.