To some extent, I think, to recognize why the post-Soviet space has not democratized, it's necessary to recognize why other places have. The so-called Western democracies democratized slowly over the course of decades if not hundreds of years, so it's perhaps fair to ask whether we might not have to wait a similar period of time before democratization really happens elsewhere. In addition, it is important to examine where democracy has succeeded and failed elsewhere in the world, e.g., in some parts of Latin America (Chile and Uruguay, for examples) and in the Middle East, respectively. In the end, I think it is a combination of economics and security concerns that has prevented full democratization in the post-Soviet area.
On the former point, those countries that did democratize, whether in the tradition of the Western nations or the later cases in Latin America, did so within an environment of relative economic health. While it is a foregone conclusion that bad economic times can cause people to abandon democracy, it might be less obvious that economic stability can foster greater democratization. In the case of the post-Soviet space, the economic situation has not been great since 1991. Although there was obvious economic growth during the 1990s, it went mostly to the top levels, where it increased wealth inequality, rather than the growth being distributed more evenly among income groups. This pattern of growth was especially true in Russia. Since 2001, energy crises due to 9/11 and the subsequent war on terrorism and the 2008 global economic crisis both negatively affected even those economics that had done well during the 1990s, with the result of democratization, slow as it might have been, being reversed and authoritarianism re-asserted.
On the latter point, Plato asserted 2,500 years ago that tyrannical rule emerged out of democracy yielding chaos and that tyrants went to war to consolidate their regimes. While the comparison to contemporary authoritarian regimes is less than perfect, it is nevertheless true that serious security concerns have arisen in many of the post-Soviet states, with the result that a decreased emphasis on diversity of opinion has been the result. For instance, where ethnic conflicts have emerged, e.g., between Armenia and Azerbaijan over Nagorno-Karabakh, there has been stunted democracy and the re-emergence of authoritarianism. To some extent, have a history of being victims of genocide has facilitated this reaction among Armenians; the sense of being besieged probably contributes to this phenomenon among Azeris. In a larger sense, concerns about Islamic fundamentalist violence could fuel security concerns in Central Asia and, during the 1990s, in Russia itself. It is more likely that Russia and Russian-aligned states fear the United States militarily and that those states pulling away from Russia fear Russia seeking to re-establish (neo-)colonial rule on the basis of protecting ethnically Russian populations. The specific fears are different on the two sides of the border, but the end result of resurgent authoritarianism is shared.