I think the "10% of people do 90% of the work" statement that Ken made is true of most clubs of any type.
You must also consider that those 10% also use all of the club facilities 90% more than other club members, so if you are using the club field more than the other members, you should expect to do the majority of the work.
I wouldn't expect the guy that comes out to the field once a month, to take on regular mowing duties. If he wants to fine, but don't force him on a mowing list, or make him pay extra dues. Let the people that use the field the most keep the field up.
Greg