There is no one reason as every situation may be unique. There are those children who are not cut from the same material. There are those with all the potential but crack under pressure. There are those who just don't care to succeed and just want to mulch off of what their parent built.
Success all depends on the individual, regardless of who your parents are. The counter question could be "What causes so many children of unsuccessful parents TO actually reach their full potential"?
No parent wants their child to fail but some children want to fail in order to rebel. Some don't care about success of failure, Some just want to be their own person and often times this leads them in the wrong direction.
Each situation warrants a different perspective.