I have been a member of two professionally run flying clubs and one amateur one.
The first professional club was based at a large airport and had a superb airport location which, with excellent food, attracted many members of the public who bought trial flights. It operated the usual fleet of Cessna/Piper aircraft. The very good social side was maintained by a large group of supporters, most of whom did not fly except as passengers. Although it was great to be a member, I have no idea how financially viable it was.
This club was sold to a national flying training organisation who completely, and very quickly, destroyed the social side. I assume that this venture then failed because it was sold(given?) back to some of the old instructors and still exists but does not appear to have regained it's former glory which depended on the social activities and excellent catering.
The second club offers good catering, a building social side but, being more rural, has to extend it's catchment area to attract enough paying customers. It does this with a good restaurant which attracts many members of the public who buy trial flights.
It would seem that catering and social activities are the key to a successful club, especially if people have to travel to get there.
Obviously a core of regular spenders can be maintained if there are good facilities for private owners e.g. hangarage and engineering.