Meta-analysis of 58 experiments concludes that the widely-held belief that women's sexual preferences change with their menstrual cycles is largely unsupported.

Memorable quote from University of Southern California's press release regarding research findings:

Fertile women may desire sex with men who seem particularly masculine or genetically fit — but no more so during peak fertility than in any other period of their cycles, reveals the meta-analysis of research led by Wendy Wood, USC Provost Professor of Psychology and Business. Similarly, when women are not as fertile — sharing certain hormonal profiles with pregnancy — they are not especially oriented towards kinder, gentler mates who can provide for their young.

The thorough review of research on the drivers of human reproduction, in the journal Emotion Review, highlights the importance of verification in the scientific method, as well as potential problems in how science is reported in the media. Wood and her team found that the correlations between menstrual cycle and mate preference declined over time, that is, most subsequent attempts to replicate the finding showed less of an effect. They also reveal that papers that did not show a link between menstrual cycle and sexual preference — that only showed no such correlation existed — were much less likely to be accepted for publication in a journal, often despite more precise methodology.

"These effects have become accepted lore. Our failure to find consistent effects of women's hormonal cycling on mate preferences does not, of course, rule out such influences. Yet our review suggests these effects are subtle, if at all present," said Wood, who also serves as vice dean for social sciences at the USC Dornsife College of Letters, Arts and Sciences. "By relying on outmoded theories that emphasize biology to the exclusion of culture, evolutionary psychologists may be missing some of the most important, characteristically human processes — our remarkable ability to exert control over our own behavior."

I cannot find the entire piece of research for free, but here's the abstract.

In evolutionary psychology predictions, women's mate preferences shift between fertile and nonfertile times of the month to reflect ancestral fitness benefits. Our meta-analytic test involving 58 independent reports (13 unpublished, 45 published) was largely nonsupportive. Specifically, fertile women did not especially desire sex in short-term relationships with men purported to be of high genetic quality (i.e., high testosterone, masculinity, dominance, symmetry). The few significant preference shifts appeared to be research artifacts. The effects declined over time in published work, were limited to studies that used broader, less precise definitions of the fertile phase, and were found only in published research.

Slate discusses findings here.