Are there cases when a woman is allowed to go to the mikveh before the completion of the 7 white days, if it is medically demonstrable that the woman’s most fertile days are during the 7 white days (let us say the 4th or 5th day), and the couple is having trouble conceiving?

Shalom U'vracha The Gemara already tells us in a number of places that women accepted on themselves that if they see even a drop of blood then they need to act as though it is ziva that requires seven clean days before going to the mikvah. This is the halacha and therefore there is no heiter for a woman to not keep seven clean days. In cases when this is critical for the purpose of getting pregnant then she should contact a Rav who will direct her how to overcome this problem. You may contact me directly at Machon Puah 972-2-65156050 and I will be able to direct you. Kol Tuv Rabbi Gideon Weitzman