The reasoning (as I recall it being explained) is that during acute stress, the body will prevent implantation, or else miscarry, due to the hormones released in response to stress. Now, any OB/GYN can explain to a Pro-Life person why this isn't the case, but like the way any lawyer could easily dismantle the Birther argument, the truth doesn't matter. The problem is how does a Pro-Life justify forcing rape victims to carry their babies to term, and the solution is to say that "real" rape victims don't get pregnant and those who claim they were raped are disproven by the fact that she hadn't miscarried. Shamefully, the second half of that justification includes dismissing the claims of rape victims who weren't assaulted in the stereotypical manner, and even then, there are doubts about the veracity of the claims.
I don't think this is what all Pro-Life people think, but this is what I heard growing up, and I never questioned it myself, as I was exceptionally naive about sex thanks to the sex education endorsed by the Catholic Church. Akin is Presbyterian, not Catholic, but in St. Louis, the Catholic Church is an intensely Pro-Life community. Any arguments made by Catholic Pro-Life groups in this area will inevitably spread throughout the movement. And now that the Tea Party is embracing a highly restrictive abortion policy, it needs people to justify the unjustifiable. If you're Akin, you go back to the pseudoscience that made so much sense at the time, and voila, instant idiocy.
This wasn't misspeaking, this was a well-trodden justification within the Pro-Life community.
Late Update: At The Atlantic Garance Franke-Ruta provides more detail on the history of this bit of politically-charged pseudo-science.