/u/vertexoflife elaborates on the origins and development of this myth here:

When and how did the stereotype that men want sex more than women begin?

It’s a very old belief, but it’s not clear it has just one starting place. The Talmud, for instance, believed women had to “seed” just as men had to “seed”. “Seed” being a commonly used Biblical expression for ejactulate, sperm, and progeny (as well as literal seeds). The verb used in the Talmud means to emit seeds, so it is often understood to mean “orgasm” or something to that effect. The Talmudic passage in question, for a child to be conceived, both the male and the female partner need to seed. This seems to be related to ideas from Hippocrates and Galen. See one of my favorite rabbi’s, Rabbi Fink or /u/e_fink, comments here on his blog, though I will admit I only know the Greek connection through him.

The Guardian has a long discussion on how this idea made its way into 21st century America. That article’s first example is this:

One of the earliest British legal texts — Fleta, from about 1290 — has this familiar-sounding clause: "If, however, the woman should have conceived at the time alleged in the appeal, it abates, for without a woman's consent she could not conceive."

The Week piece doesn’t actually trace that many pre-modern examples, but it does make clear that it was incorpated into early modern medical knowledge:

Samuel Farr's Elements of Medical Jurisprudence, a treatise from 1785 (second edition 1814), elaborates: "For without an excitation of lust, or the enjoyment of pleasure in the venereal act, no conception can probably take place. So that if an absolute rape were to be perpetrated, it is not likely she would become pregnant."

This article in the Atlantic implies strongly that it’s likely the idea came to Aiken through anti-abortion activists, as this idea was in several publications and statements in the 1980’s and 90’s. It seems like possibly this was not common rhetoric before this point, as the “Religious Right”, including a new Protestant focus on the previously mostly Catholic issue of abortion, only really emerged as a powerful force in the 1980’s. There is clear continuity between the 19th century (and earlier) understandings of women needing to “seed” and the post-80’s “legitimate rape”-type comments, but I don’t know anyone else who has quite followed through all the connective tissue (much of which might be oral and from activist political trainings).

The most likely source of bridging seems to be Fred Mecklenburg’s 1972 article “The Indications for Induced Abortion: A Physician's Perspective”, which incidentally Akin specifically cited. In fact, it was the only thing he cited, seemingly indicating that this article was particularly influential to the movement. It focuses on trauma, and makes no explicit mention of women “seeding” (beyond normal cyclical ovulation).

The trauma of rape was only one part of Mecklenberg’s argument. From the St Louis Today article above:

The reasons were numerous: Not all rapes result in "a completed act of intercourse," Mecklenburg wrote, adding that it was "improbable" that a rape would occur "on the 1-2 days of the month in which the woman would be fertile."

Mecklenburg's third reason seems to have been picked up by Akin.

A woman exposed to the trauma of rape, Mecklenburg wrote, "will not ovulate even if she is 'scheduled' to."

[…]Finally, Mecklenburg said it was likely that the rapists — because of "frequent masturbation" — were unlikely to be fertile themselves.

I haven’t looked at the original article, but Mecklenburg’s two pieces of evidence seem to be:

1. police statements (In Mecklenburg's original article, he wrote that pregnancy resulting from rape "is extremely rare," and cited as an example the city of Buffalo, N.Y., which had not seen "a pregnancy from confirmed rape in over 30 years." Other cities — Chicago, Washington, St. Paul — also had experienced lengthy spells without a rape-caused pregnancy, Mecklenburg wrote), and

2. Nazi medical experiments in concentration camps (The Nazis tested this hypothesis [that traumatized women don’t ovulate] "by selecting women who were about to ovulate and sending them to the gas chambers, only to bring them back after their realistic mock-killing, to see what the effect this had on their ovulatory patterns. An extremely high percentage of these women did not ovulate.").

These specific Nazi experiments seem to have not actually taken place, but are seemingly based on the research of Nazi (or at least Nazi-era) scientist Hermann Stieve, who actually did find that trauma made women ovulate less predictably but doesn’t appear to have studied the effects of rape directly (it also appears that all of his subjects were executed prisoners, most political prisoners, from the Plötzensee Prison in Berlin, and not concentration camps never mind ones with gas chambers, which were outside of the German Reich). (Continued below)

This is a great article about the nazi history of this belief.