In a pyramid scheme, the participants are mostly busy recruiting new members, and the tangible benefits of membership are tied to the stream of recruits. Once that stream stops growing, people start dropping out and the same pyramid structure that accelerated the growth also leads to accelerated collapse.

Religions that have endured over generations have a very different balance of promises and recruitments. Instead of large immediate rewards that can't be kept up over the long term, they rely on hopes about the indefinite future (e.g. paradise) or benefits that are proportional to the size of the community, not it's growth over time (e.g. caring for their sick). Religions do rely on missionarizing to grow, but they can remain stable even without growth, and mostly propagate themselves by parents converting their children.