Intriguingly enough, it has been noted that China in the past few years has been allowing more and more capitalism within the country. It's still nothing like America, but clearly they recognized that communism is now a means of maintaining power - not a realistic vision of life. Some guys like Lenin may have really believed in in, but I think most modern Communist dictators actually do realize that it's a failed dream and are simply keeping themselves in power.
Anyway, on topic: the thing is, democracy isn't dying, per se. However, it is changing drastically. While I mostly agree with President Bush, some of the things he has done would have been shocking even a few years ago; moreover, the power of the government is increasing exponentially every year. And that doesn't matter whether it's a Republican or a Democrat. I think that that is the danger; in a situation where the people depend on the government instead of the other way around, it is very easy for the government to suspend rights if "it has become necessary." For example, the Patriot Act in the US. A good idea, but even though it hasn't been used wrongly (yet) it was reactive, and gave the government way too much power.
I think the greatest threat to democracy, at least in America, but probably in general, is judicial fiat. In America, it's liberal judges (see the 9th Circuit Court of Appeals) that are doing it, but it would be just as bad and dangerous to have conservative judges doing it: legislating. It is not the place of the courts to make law, but that is what they are doing. For example (and don't get a debate on this started here, please), the Massachusetts Supreme Court has decided - against the will of the majority - that gay marriage is not only legal but, in essence, mandatory. These are unelected officials who, at this point, have no check on their power to legislate except that the case has to get to them. In our sue-happy society, that means they get to touch almost every part of society. In the Federalist Papers, James Madison explicitly warned against the problems with such a situation, noting that if it ever happened, America - and any democracy - would be in serious trouble. The only check on judges is impeachment and/or constitutional amendments - and impeachmetn is not an option now, because what they are doing is not technically illegal...
Such a governmental institution - an oligarchy of the judicial branch, if you will - is the greatest threat to democracy that there can be, unless a President were ever able to completely seize power, which is unlikely for many years.