Why are there still poor people in America half a century after the implementation of a system of social welfare programs that were designed to end poverty?
The way a person answers this question depends largely on their political ideology. Therefore, there are many possible answers.
A conservative might argue that poverty persists precisely because of those programs. Such a person would say that welfare programs have encouraged poor people to develop bad habits in which they rely on the government for help. The poor would be better off if they would be made to find work and develop the habits that lead to success.
A liberal might argue that poverty persists because the social programs you mentioned have been too limited or have not been done in the right way. Such a person would argue that our government does not do enough to help poor people obtain child care so they can work, or get job training so they can find a good job. Such a person might argue that the government has not done enough to help poor children get a better education.
So, depending on one's political ideology, one can attribute the persistence of poverty to excessive government action or to lack of government action.