I expect technology to advance to a point where abortion will be completely unnecessary, and thus banned.
Something like this, except for the last line. Fetal defects will be curable in the womb, and IUD-style technology will be advanced to the point that unexpected pregnancies will be much, much more rare in the developed world. That being said, I still don't see it being banned outright.
I think that abortion would be banned at that point because, if it's completely unnecessary and there isn't really consensus about whether a fetus is a person or not, it would be better to err on the side of caution and not risk killing a person.