Thinking about your original post some more, I'm wondering if perhaps fun groups tend to involve flow on the part of many participants?
If that's an element of it, it would seem an inherently delicate arrangement, because flow requires people to be challenged, but not too challenged, and practice in those circumstances frequently produces growth in skills and a need to increase the level of challenge. If people grow at different speeds they might need different challenges and no longer find association productive. Or you might have a cohort with an initial common understanding that stays roughly synced who "use up all their challenge" and end up either becoming bored or trying to figure out a new mission that will actually be interesting to work on.
If this is true, then it suggests that really hard games with effective handicapping systems might be a good thing to build into a community? If some people get better fast, the can just aspire to winning with a higher handicap. If the game is really deep, there's room to improve for a long time. This makes me wonder if maybe golf clubs or go clubs tend to be long lived?
I feel like I'm groping here... Like a better conversation on this topic might have more data points in the form of stories about organizations and their tendencies. Then a good theory (a theory I don't feel anywhere close to proposing or justifying at the present time) would be able to give some kind of causal/mechanistic summary of all the data, and there would be parts of the theory that spoke to "fun" and how it related to all the rest of what happens in different organizations.
I suggest that there are default patterns for social groups, and they could be viewed as high entropy-- what you'd expect without knowing more than that there was a social group of a certain size, possibly with some modifications for tech level and status.
For example, I think that authoritarianism is the default for government-- "we're in charge because we're in charge, and it would be dangerous for anyone who tries to change that". Totalitarianism is lower entropy-- it's surprising for the people in charge to have an ideology which requires them to make drastic changes.
The recent Elitist Jerks: A Well-kept Garden describes an effort to fight one sort of entropy (the repetition of the same questions and answers) which resulted in another sort of entropy (an excessively stable and eventually fragile core group).
Maintaining fun is another challenge in the keeping things alive category. Pleasant is relatively easy. Fun (which I'd say requires novelty) is harder, and I'm interested in comments on what it takes to keep the fun going.
There's a theory that life exists as chaos on the border between order and randomness-- I find this plausible, and it's a different angle for looking at the Friendliness problem. How can a system be built which continues to permit (or even encourage) interesting sorts of change, without permitting change so drastic that we as we are now wouldn't recognize the outcome as still related to us?