In most small towns the same small group sits on every board, and the institutions are only as durable as their willingness to keep doing it.

The usual complaint is that nobody volunteers any more. The usual reality is that a handful of people are doing six roles each and have no capacity to train anybody, so the barrier to joining is unintentionally enormous.
Most volunteer organisations keep their operating knowledge in one person's head. When that person steps back, the organisation does not transfer — it restarts. A written-down procedure is the single cheapest form of continuity available.
People decline open-ended board roles and accept defined jobs with an end date. Organisations that split work into discrete tasks recruit far more easily than those advertising for committee members.
Small-town organisations usually fail for lack of hands rather than lack of funding. Grants are often easier to obtain than a reliable treasurer, which is why so many well-funded local projects quietly stop.
Unpaid work that is never acknowledged stops being done. The towns that keep their volunteers are the ones where the work is visible, named and thanked, routinely and in public.
One part-time paid coordinator frequently does more for an organisation's survival than a dozen extra volunteers, because the coordinating work is the part nobody wants to do unpaid. Small grants are often easier to get for this than people assume.