Partial-Birth Abortions are one of those issues on the slippery slope that pro-choice advocates don't want to touch because their argument starts to crumble. If you look at the term "Partial-Birth Abortions" a priori - that is, by pure reason - you come to the conclusion that something is in the process of being born (partial-birth). This thing being born (excuse my use of the word thing), must be alive in order to be born. Actually, it may be still-born, in which case the "Abortion" part of the procedure would be unnecessary, but we know it is. So, the abortion terminates this thing that is alive.
Up until this point, there still is no definitive evidence why partial-birth abortions should not occur. After all, we kill living things all the time - chickens, cattle, or even chicken embryos (eggs), trees, etc. However, there is a universal moral/ethical rule that the killing of human life is not just. So if we accept this universal moral/ethical rule, and we can prove that this "thing" being born is human life (i.e. it exhibits the tell-tale characteristics of human life - the main one being thought), then we can prove that partial-birth abortions are simply "wrong" without having to prove that abortion as a whole is a black-and-white, "right" or "wrong" issue. Well, this is a trivial task. Towards the end of the second-trimester, to the beginning of the third-trimester, when most (if I'm not mistaken) partial-birth abortions occur, the fetus has observable human brainwave activity. We know that this brainwave activity is a byproduct of thinking and that the absence of it implies that there is no "thinking" going on - i.e. many doctors use this to declare a brain-dead patient and cease all efforts to keep him/her alive. Well, since there is brainwave activity going on, this implies that this "thing" is human life and therefore must be protected under the same rules/laws and with the same rights as any other human life.
The above, is largely the opinion of Carl Sagan, much of which I tend to agree with. Although, being pro-life myself, it is uncomfortable for me to accept that early-term abortions can be justified (in this case, with the absence of brainwave activity), it is as close to a rational determinant on this issue as I've seen. Because something is uncomfortable, does not mean it is wrong. And, I have no concrete evidence to argue against early-term abortions. Of course, it is arguable whether additional human characteristics can be observed at an earlier point in the pregnancy, thereby making abortions wrong by Sagan's logic even at earlier points in the pregnancy. However, keep in mind that these characteristics must be uniquely-human. I for one, after trying to search for a uniquely-human characteristic other than thought, can't come up with one. Mind you, even thought is debatable as a uniquely human characteristic, unshared by the animal world. But one thing is certain, that human thought is orders of magnitude more complex than even our closest DNA relatives. That being said, I'm sure the complexity of this thought can, and is, observable in the brainwave activity.
-GL