If only we knew the answer to this… There is no way to answer this question that is objectively and provably correct. If we could answer it, then we would know how to help countries democratize. Instead, all we can do is to theorize.
It seems that countries are more likely to democratize successfully if they have a large middle class. It seems that middle classes (people who have enough money so that their basic needs are secure but who are not really rich) are more likely than the rich or the poor to care about democracy.
It seems that countries are more likely to democratize successfully if (at least at first) they have relatively homogeneous populations. Countries that have deep religious or ethnic splits have a harder time democratizing (we may be seeing this in Egypt right now). They seem to have problems because the different groups do not trust each other and therefore do not want to work together in a democratic society. They would prefer to try to use the government to hurt the other group.
It seems that countries are more likely to democratize successfully if they are given a long period of time in which to do so. If countries are being pushed to immediately become fully democratic, they have a hard time. They need to have time so that they can build the institutions and manners of thinking that are needed for democracy to truly take hold.
These are some of the factors that seem to make it easier for countries to become democratic. But it is not clear if these are hard and fast rules and it is not clear if there are other requirements needed for countries to become liberal democracies.