Being out here in flyover country, I think difficulty can hurt a club's chances of getting members if it isn't the "A" club in town.
I live in Topeka, KS, where we once had 4 country clubs. Now, there's really only one, and it's the least enjoyable course in town. Although it was designed by Perry Maxwell, now it has really, really narrow fairways, lined with thick rough and hundreds (thousands?) of mature trees that were planted some time in the 1940s as near as I can tell. But they're still doing OK for membership.
Where I play, the course is much more difficult--especially from the forward tees and "men's" tees--than the two courses operated by the county. And since we've been the "B" private club for some time, we struggled to maintain membership numbers. I know a number of people who could have easily handled the paltry $100/month dues, but found no fun to play because of narrow fairways and tall rough.
They all found the two public courses more fun to play, without even thinking about the fact that they are wider, have lower rough, and are 400+ yards shorter from the red tees and white tees respectively.
Hutchinson, KS is another place where there's a hard course that's the "AAAAAA" course doing pretty well. There's also a "B" course that is actually more difficult for most golfers, and it's barely scraping by. (Imagine PD with 25-yard wide fairways and trees in the rough, and you'll get an idea of what Highlands is like.)
K