Bryan picked up on the fact that what we call intergenerational "economic mobility" (or lack thereof) is very much a cultural phenomenon. I would like to add that marriage patterns play a role, too. If economic classes become more endogamous (tending to marry within a well-defined social group), "economic mobility" will appear to decline. The traditional artistocracy maintained itself through endogamy, and my impression is that the new economic aristocracy practices endogamy even more strictly.
In fact, I have long suspected that the contemporary significance of education is driven in part by endogamy. If you are in the affluent social group, and you want to make sure that you kids stay there, send them to a schools that sort students into gifted-and-talented classes, and as long as those classes are stocked with kids from other affluent parents, you're likely to see your kid marry within his/her social group.
If social engineers really wanted to increase social mobility, they would enforce more randomness in mating. One way to do that would be to abolish the gifted and talented track, including elite colleges, and instead maintain social contact across economic groupings. I am not saying that I want this social engineering project to be undertaken, but I am just trying to be forthcoming about what it involves.