Why would we grant a rape exception to an abortion ban?
Let's take the pro-life side at their word that their overriding concern is the protection of human life, and that in their judgment the fetus's right to life outweighs the mother's interest in not having it. Given such premises I think it makes absolute sense to say, as a number of prominent Republicans have, that a person's right to life is not contingent on the circumstances of their conception. After all, after the child is born -- when pro-choicers would agree that the child has a right to life that trumps the mother's interests -- we would not condone infanticide if the child was a result of rape. "It sucks that you got raped, but don't punish the child for that" seems to be the only coherent position for someone who puts a fetal right to life above all else.
But of course the point of bringing up the rape exception is to push people to question whether a fetal right to life should trump everything else. Imagining the horror of being forced to carry your rapist's baby ought to lead a person to think that the mother's interests should sometimes override whatever rights or interests the fetus has. The "problem" here is that once you start down this road of emphasizing the mother's interests, there's no good reason to stop at just allowing an exception for rape. There are lots of non-rape pregnancies that can be just as traumatic, difficult, and negatively-life-altering as a rape pregnancy. It seems exceedingly unlikely that the moral weight of the various interests are so perfectly balanced to make rape, and only rape, the case where the mother's interests take precedence. This line of thinking on its own does not necessarily lead all the way to a policy of publicly-funded abortions for anyone anytime for any reason*, but it certainly takes us to a much more liberal place than just a narrow rape exception. In this light, support for a rape exception starts to look like a political ploy to cut off the effectiveness of this line of pro-choice logic, rather than a principled position on what abortions are acceptable.
Moreover, even if rape were the only situation in which the mother's interests took precedence, establishing that as a rule would backfire. The point of a rape exception is to spare the mother the trauma of carrying a child conceived through rape. Since people desperate enough for an abortion to resort to unsafe methods like coathangers would also surely be desperate enough to lie about having been raped, you would need a system to verify that an abortion-seeker had actually been raped. This system would necessarily exacerbate the trauma of rape -- forcing the victim to recount her story to an unsympathetic and stereotype-bound justice system. There are good reasons that many rape victims are reluctant to go to the police, after all. A more liberal abortion policy would spare rape victims this additional burden.
Nevertheless, I think there are two ways of looking at the abortion issue that do provide a foundation for a rape exception. Unfortunately, neither is a particularly attractive philosophy to espouse in public (though there are people who do).
First, if restricting abortion is about punishing sluts, then a rape exception makes sense. Abortion is wrong, in this view, because having sex outside of married heterosexual procreation is wrong, and it's women's responsibility to put the brakes on. So illicit sex ought to carry a risk of pregnancy, and someone who has illicit sex ought to suffer the consequences. Rape is an exception because a rape victim did not choose to have the pregnancy-causing sex. This exception has to be limited to a small category of "legitimate" (Akin) or "forcible" (Ryan) rapes, since many alleged rapes are held to be products of the victim's own sluttiness and thus her own fault. But in the abstract, a rape exception makes sense as a way of not punishing those who truly aren't responsible for the illicit sex they had.
Second, if restricting abortion is about control over other people's uteruses, then a rape exception makes sense. In this way of thinking, a uterus doesn't really belong to the person whose body it resides in, it belongs to society as a whole, and specifically to the dominant male class of that society. To get an abortion, in this view, is to exercise your own selfish control over a public uterus -- a sort of insubordination. But rape is also insubordination, this time by the rapist, who is claiming access to a uterus "out of turn," in contravention to the prevailing social order's rules. (Again, this logic is limited to "legitimate" or "forcible" rapes that fit this acting-out-against-the-hierarchy model.) A rape exception allows this insubordination to be wiped away.
In summary, a pro-lifer who genuinely thinks the fetus's right to life is paramount has to bite the bullet and hold that the mother's interests are trumped even in the case of rape. Someone who wants to give real consideration to the mother's interests has to allow abortion much more broadly than just in the case of rape. But people who want to punish sluts and control uteruses can make a case for a rape exception.
*"Publicly-funded abortions for anyone anytime for any reason" pretty well describes my own position on the issue.