No matter how you want to twist things around abortion is murder and murder is wrong. Partial-birth abortion is even worse because the baby (or fetus to those who will not admit it is a baby) has survived the first trimester of pregnancy. At this stage of development, the risk of miscarriage has decreased substantially. If you want socio-economic reasons to ban partial birth abortion, consider the health problems that can be caused from an abortion gone wrong. Additional health concerns create additional health expenses. There are plenty of families who want babies and are unable to have any of their own. These families are often willing to adopt (which includes paying medical bills) or even to buy a baby illegally. Having these children instead of killing them off shows more love and mercy for the children. It also gives the child a chance to be loved and raised in an environment where they can have a better life. Adoption shows love for a child. Abortion does not.
Women that have low socio-economic status are more likely be pregnant at too early of an age, or while abusing drugs, alcohol or tobacco. These women are also very unlikely to have access to good medical care, especially preventative care. In many of these situations, a partial birth abortion would be preferable to entrusting the care of severely disabled babies to these individuals.
**Note - "their" is not the correct usage of "there" in the question title.