I'm in a MOMS Club with about 40 members too, and probably only about 15 participate in anything in a given week. I'm on the activities committee, and we ask for suggestions from the group each month, and we try to schedule lots of things (at least 5 a week, and more in the summer) at various times of day to meet everyone's scheduling needs. We do have age-specific playgroups, as someone below mentioned, and, though I think that's necessary when a group gets as big as ours, I think it's also divided our group into smaller cliques, and that's not a great thing. Those playgroup people tend to get together on their own on non-playgroup days and do things without inviting others, even though there's something on the calendar for the whole group. I don't know if your group is having that problem or not, but it's something we've encountered and honestly we haven't figured out a way around it. We can't tell people they aren't allowed to meet outside of the club, and we can't make people be more social.
I once went to a MOMS Club banquet and the speaker said that if your club has an activity and only 10% of the group attends (for us, that's 4 people), you've still provided a social activity for 4 people (plus their kids) who otherwise would have been home doing nothing. When I think of it that way, it makes me less irritated about the huge number of people in our club who don't come to anything.
I guess I don't really have a solution for you, but know that you're not alone in your frustration!