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Alexei comments on Selecting optimal group projects and roles - Less Wrong
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This could be easily explained by a limited number of people who would be interested in that church. Probably, after you get to 200, you've reached out to most of the people you could, so the growth rate slows down.
To check this: split a church with 200 attendees into two churches with 100 attendees each, and see if their growth rate improves.
Lending support to the theory that it's 'just' a matter of size: Dunbar's Number, which is 150-ish for humans.
With margin of error 60-ish
In the sense that we don't know what the actual average is for humans, or in the sense that the bell curve for Dunbar's number for individuals is rather flat?
This could be true, but I don't think so. In my experience, church size is much more strongly influenced by other factors, like how leadership draws the boundary lines between church units, and which geographic area people who are already current members decide to move into. That said, you have the perfect test.