Contrary to left wing stereotypes, keeping one's kid in the same class is hardest for the upper class.
Analyzed a different way, some 43% of those raised in lower-class families remain in the lower class, while 60% of those from middle-class backgrounds stay middle class and 33% of those from upper-class families remain in the upper class.
Makes sense. Regression to the mean for offspring IQ is a huge problem. To put it another way: The majority of kids born to really smart people are not as smart as their parents. So smart people who manage to use their brains to make a lot of money are mostly going to have kids who do worse in school and worse in the marketplace.
Once upper class people gain the ability to choose embryos based on genes for intelligence and personality type it seems likely that downward social mobility out of the upper will become less common. Upper class people will choose their mates partially based on genetic endowment. Women of lower classes might opt to use sperm donors from the upper classes once we reach that point.