I used to fast through my cycle, and also weekly. It is actually a good time to do any kind of cleanse or fast because that is when a woman detoxes. It has made that time a ton easier for me as well.
Although I wouldn't recommend long-term or extended fasting (like more than a couple of days) while working or any kind of activity, it is a great time to rest (and for some a spiritual time of prayer), if you aren't taking in any calories it's not suggested to expend any energy. It's amazing how much a body will repair and heal in sleep. Body builders always get extra sleep as their muscles grow when they rest.
You may want to consider doing a juice feast, which is getting a good amount of calories through juice. I did it for a short time and felt wonderful.
http://www.rawreform.com/content/view/271/137