This is one of the better topics I've seen on the board so far!
My own experience is that I've been bowling off and on in various leagues for somewhere around 30 years. And when I look back on league I've been in and why I quit or didn't come back the following year, one reason does stand out.
The most common, as others have said, is the same teams winning over and over, or there being such a huge and obvious imbalance that it leaves no one else a chance.
In most of the leagues I've been in, I've never signed up "with my own team". I've always had to sign up as an individual, because I don't have friends who bowl. So it always became luck of the draw, and I always got put on whatever team happened to need a bowler, and I never had any say into the matter. And of course, the people who were putting the teams together would take the best bowlers availabe for THEIR team.
So I usually ended up on a team with the kid just learning to bowl who had a K-Mart bowling ball with 3" finger holes and who threw every other ball in the gutter - and the old lady with the 85 average who threw the ball at 3 mph down the lane. After 3 weeks of getting 100 pins in handicap and still losing every game by 100 pins or more, one comes up with an excuse why they suddenly can't bowl anymore. This has happened to me more than once.
So, yes, the competition factor will make people not want to bowl when they have no chance.
What can one do? I don't know. Its problematic to have such an imbalance in my opinion that the top 5 or 6 teams will win every game and the bottom 5 or 6 will lose every game, with the teams in the middle going 50-50 and having no chance. But when people are friends and have been bowling together for awhile, don't you have to allow them that?
My thought was to have a draft league. Use established averages from the previous year, select team captains based on the highest averages from the previous season, the get everybody together and do an old-fashioned choose up. Then no one can change teams once picked, except by a 100% captains vote. This would break up the high average teams and make it more fair all around.
The problem with it is that people will complain friends have to be allowed to bowl together, and some or all of the more experienced players, especially those who've been winning and winning, woul dnot like it and quit. This is bad because most of those people are going to be your treasrer and secretary, etc, as the most experienced people.
But this was the only solution I saw to this problem.
Again, GREAT topic.
"Bowling should be played by bowlers, not physicists." - CoachJim