Teams break up in all levels but my observation is that lower tier (2,3, SE, S,B) teams have higher frequency of breakups.
Top tier teams appear to have kids trying out throughout the year and as long as its winning, they tend to stay together. It appear to have no relationship with how good or bad families are, or for that matter the quality of coaching. Unfortunately, most parents equate winning team coach=good coach, so as long as the team is winning, its all good.
The youth sports parents falls into, typically, between two ends of spectrum. On one end, the gypsy type moves from club to club in search of better every year. The other end has the community type who tends to stay together because kids are friends. Since most people falls somewhere in between, the likelihood of any given team breaking up probably has to do with how large of population a team has close to the gypsy type of families.
The other large factor is the players quitting the sports. As the team reach U15+, attrition becomes an issue. Our younger kid's team has two players quitting and not coming back from the high school break. Had 18 players, now 16 and we know couple of those kids are moving on so will be down to 14. Since we have two keepers, in reality, we have two field subs. Very common as kids get older.