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The reasons for the Demographic Transition are complex, but it has been a fairly good model for predicting population dynamics, at least the order, if not a time-frame. Nearly every country is passing through, or has passed through the demographic transition. As can be seen in the map (yellow: finished demographic transition; orange: late demographic transition; red: early demographic transition), there are already many countries which have passed through the four stages of demographic transition. In fact, nearly half of the world's population lives in such countries, a number which will most likely increase in the future.
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What this means is that in the near future, the majority of the world will live in countries for which there is not an effective model for predicting future growth. The Demographic Transition model itself suggests that upon reaching stage 4 the population growth will remain roughly static. In the long term, this may well be the case, but the issue is that alternative possibilities do not seem much-considered.
The most important projections of the next 50 years are those which come from the United Nations Population Division (http://esa.un.org/unpp/index.asp?panel=4). These projections work under several assumptions, which are described in the above link, of which one strikes me as questionable: the UN shows high fertility, low fertility, and medium variants of population growth over the next 42 years, in which the fertility rate are assumed to converge on a single rate:1.35, 1.85, or 2.35 children per woman. This seems pretty odd, especially considering that no country has yet to have a particularly stable fertility rate at any level. Part of this may be wishful thinking, as a fertility rate of around 1.85 (medium variant) is just below replacement and would eventually lead to a very slow decline in population.
Basically, the UN predictions (and other such predictions) assume that once a country reaches a certain stage in its development, its once dynamic demographic structure freezes, in the long term. I would say that the model is much too uncertain for that, largely because of the simple fact that demographers have very little experience with stage four of the demographic transition in the long term. Only in the 1970s did most of Europe's (http://www.ihs.ac.at/pdf/soz/macinnestabs%20and%20fig.pdf), Japan's (http://www.un.org/esa/population/publications/migration/japan.pdf) and the USA's (http://en.wikipedia.org/wiki/Demographic_history_of_the_United_States) fertility rates pass below replacement. Therefore, it's sensible to at least be open to the possibility that total fertility rates will do something other than remain static.
It's possible that they will continue to drop.
The first countries to pass through the demographic transition (Western Europe and the USA) mostly have not fallen very far below replacement. Few passed below the threshold of 1.5. However, the more recent countries to reach the fourth stage of the demographic transition have reached much lower rates. It may even be that every Eastern European, Southern European, and East Asian country which has been in stage four for 10 years or more has at least had a fertility rate of 1.5 or lower, while none of the earlier countries have done so (in order for this to be true, one must consider Germany to be an East European country. A bit of a stretch, but demographic and cultural borders need not be exactly the same). This may be accounted for by swiftness of transition; The countries of Western Europe and the USA took much longer to pass into the fourth stage of the demographic transition than those of Eastern Europe and Eastern Asia. Might that mean that these countries will stabilize their populations at a lower fertility rate? Would that mean that the next countries (such as Iran, whose fertility rate has gone from 7 to 2 in just twenty years) would stabilize at an even lower level?
Perhaps rates will rise again.
If one believes that the demographic transition is, in fact, a transition, with demographic stages through which one must pass through in the proper order, then a look at the future might best be found in the countries which first past through the transition: Western Europe and the USA. Judging by the three most populous countries in this group, the USA (http://en.wikipedia.org/wiki/Demographic_history_of_the_United_States), the UK (http://news.bbc.co.uk/2/hi/health/6729953.stm), and France (http://en.wikipedia.org/wiki/Demographics_of_France), it is possible that rates are already rising. The fertility rates in the USA have been tentatively rising for over thirty years, from around 1.75 in the mid-70s to around 2.1 today. The trend is more short-term for France, but more dramatic, with a rise from 1.66 in the mid-90s to nearly 2.0 today. For the UK, the possible trend is even smaller and shorter, rising from a record-low 1.63 in 2001 to around 1.85 today. These trends are not much, but they give some idea of how dynamic demographics remain.
I do not claim to know the trends which countries will follow after the fourth stage of the demographic transition. However, I do believe that trends will eventually emerge and the demographic transition model will eventually be modified.
The demographic Transition graph was taken from bbc.co.uk.
The Demographic Transition Map was made by TheDauds