I commute most every day, period or no period, but it doesn't bother me much. That said, my inner thermostat goes a little haywire for a few days, so I have to wear more clothes and be careful not to get too hungry or I'll freeze. I also have a lower pain threshold and get sick easier, so I ride but just ease back on the intensity for a few days. Looser clothing makes it a bit more comfortable.
But I'm not sure if you're asking how to simply keep commuting during your period, or how to keep up your performance. Performance improves by riding hard at times, and riding easier at times, to let your body heal from the high intensity rides and then improve. I think most all training philosophy agrees that the only performance that can be maintained regularly at all times is a mediocre one. You do actually need the "slow" days at least as much as the "fast" days, if you want to get faster.
The racer dudes on my Norwegian bike forum are forever griping about how they get passed on their "recovery days" by silently crowing commuter warriors, and how it kills them to not speed up and leave them coughing in the dust
Winter riding is much less about badassery and much more about bundle-uppery. - malkin
1995 Kona Cinder Cone commuterFrankenbike/Selle Italia SLR Lady Gel Flow
2008 white Nakamura Summit Custom mtb/Terry Falcon X
2000 Schwinn Fastback Comp road bike/Specialized Jett