After studying various religious movements, I have found a pattern. When the movement begins, all of the members are converts. They strongly believe in the ideas put forth. The founder is alive and well, and everyone has a figurehead to look to. When the founder dies, doesn't matter how, there is a bit of chaos. People are not sure who to follow now. (they are so used to following, it doesn't occur to them that they maybe shouldn't have a leader).
Once that is resolved, the group (or groups) remaining settle happily in their new groove. They rely heavily on the founder's teachings and so the new leaders have a lot less weight. The people stay very close to at least the spirit of the original movement, or at least one of the resulting groups do. But, here comes the shaft. All of these people have children. Unless this is a universal movement where every single person feels spiritually uplifted and edified by it (hint, I don't think this has ever existed), there are going to be some children who do not fit in with the regime. There are a few different types, although it partially depends on the type of group. One set might just up and leave. Another may be an apathetic bunch, who wish to please, and so they stay on, but don't really have any true conviction about their beliefs. Another group may be angered by what is taught and will either stay in and try and destroy it, or leave and try and destroy it.
One last group. The size of this group depends on the overall appeal the movement has on the average person. These people are the same type of person as their parents. They would have converted to this belief if they had not been born to it. If the new religion is at all strange or different or shocking to the average person, this group will be fairly small. The make up of the group starts as 90% or so people who really believe in what they are doing. Once their children grow up, it changes to 80% or so (assuming that this is a strange religion where few (25%) of the children fall into the true believer status and each family has 3 children or so ... and it's an island so that no one can leave). The original adults are still around, so the overall feel of the group is very similar, for now. The next generation is born, grows up and starts to have children. It has been 40 years since the founder died and the group was out on its own. Many of the original members are dead, the ones who were 20 when the founder died, are now 60. From my pseudo-math I get about 40% true believers.
Once all of the original members are gone (about 80 years), the false percentages are gone and it falls to almost exactly the percentage of people that the religion truly appeals to. In this case 25%. Interestingly, this also corresponds to the time when those who have never met the founder of the religion are in charge. So, what does this mean? It means that after 80 years the religion in in the hands of those who do not care about the beliefs of the founders.
Majority rules, even when it's not an official democracy. By forcing/encouraging their children to stay in their religion, it was killed. The flavor of the religion changes at this point, becoming more acceptable to that part of the population that is more numerous. The ones who stayed in the religion because they didn't want to bother finding something else. Now that the 25% of true believers are longer the target for this group, it changes into what the majority needs, as it should. But that 25% for whom the religion was founded are out in the cold with nowhere to go.
What do you think happens? They go off and join the crowds of non-affiliated members of society. A couple of them go off and start their own religion, and in time one of them will gain some ground and it will take off, and all of the people drawn to that idea will join. Then they will have children who will be forced (through brainwashing) to join as well, and the cycle will begin again.