Women produce strong pheromones during their periods, that are subconsciously detectable by both men & women. Studies have shown that women who live together for a while, such as in college dorms, tend to involuntarily synchronize their periods to all occur at the same time. Pheromones are thought to be the signal that prompts this outcome.
I'm not aware of any studies linking male behavior changes to female menstrual pheromone production. It wouldn't be inconceivable, however, and you might be a good subject for a case study.
At the same time, I wonder if there's a psychological component. How do you know when she's having her period? Does she tell you? Or do you deduce it from a change in her behavior, perhaps exhibiting some PMS?
Some men do experience a false pregnancy phenomenon, getting morning sickness and labor pains, when their wives are expecting. Perhaps a similar thing can happen when around a woman known to be menstruating. Curious. I agree with GQ -- keep some tampons handy.