There are organizations that host online communities that have been or are now successful that have also been able to get away with not making a full time paid employee responsible for the community. Managing, growing and moderating the community just falls to whatever time other paid people can make available, and to volunteers.
I don’t think anything is wrong with that, necessarily. But what I notice is that when things get stale or activity declines, what happens is that some of these organizations throw a software update at the community. A redesign, new software, a substantial upgrade in feature set – something along those lines.