That's very interesting considering Atheism/Agnosticism is the highest growing demographics in the last century. I tried searching that on Google that, but mostly found many religious apologetics websites "claiming" that atheism is in decline. However, I did find this pew research article (
http://www.pewresearch.org/fact-tank/2015/04/03/why-people-with-no-religion-are-projected-to-decline-as-a-share-of-the-worlds-population/), which is respectable. Their argument seemed to be centered around the fact that the countries with high proportion of atheists have low birth rates. This is a fair analysis but it ignores why people turn atheists in the first place, its not a race where you can only be born an atheist, so future demographic estimation may not be accurate.
Furthermore, another reason they argue is the estimated population growth of mainstream religions like Catholicism and Islam. Now for Islam, it is true that Muslim-maj countries had very high birthrate in the past few decades, as a result you have a huge young Muslim population (in Iran and Pakistan for e.g.) which is one of basis for population estimation. However, fertility rates in Islamic countries have declined (and trending towards western countries), and there nothing to say that these young people will stay Muslims (or at least fundamental Sharia-loving Muslims) later on. Look at the rising reform movement in Iran, in which the youth population have large factor.
For Catholicism, I don't know whether the surveys are accurate. It depends on how people count a Catholic. Richard Dawkins addressed this vaguely in his speech against Pope Ratzinger (
https://www.youtube.com/watch?v=q_0kFU7IfPM), a lot of the time the Church uses Baptismal figures (people who are Baptised), not necessarily who are still Catholics. Now one can assume that a respected polling organisation like PewResearch would take that into account but even if it did, birth rates says very little about future Demographics estimations of Catholism and hence atheism/unaffiliated. The higher birthrates in Catholic also seem to be from Sub-Saharan African and Latin-American countries (which are also trending towards "western" countries).
If the secularist/reformist "movements" in countries like Iran, Bangladesh, Ireland, Turkey (before Erdogen) show that having high birth rates, a majority religion and a younger population of a religious sect (compared to non-religion) is not necessarily a justification for saying atheism (or secularism) is in decline.
Surely that could mean "moderate" Christians and Muslims denounce it as result?
Now, a lot of demographics changes seem to be about population growth, not population de-conversion/conversion rates. It is also possible to an atheist/secularist and still be "affiliated" to a religion. It is also possible to be an atheist/secularist and still be religious (although that happens in relatively rare occasions, so that's negligible).