Q. What is the reason and source that women as opposed to men avoid doing certain melochos and work on Rosh Chodesh?
A. Pirkei D’ Rabi Eliezer (45) mentions that when the women refused to contribute any of their jewelry for the making of golden calf, for their strong convictions and messiras nefesh, Hashem rewarded them with true simcha and joy, including Rosh Chodesh
Similarly, Tur (O.H. 417) further explains that the Sholosh Regalim, Pesach, Shavuos and Sukkos, corresponding to different seasons, represents and stand each one also for one of our unblemished Avos. However, when the next stage came to be, the Twelve Shevatim or Tribes, due to the sin of the eigel, did not actually made it by themselves without the help of their unblemished women, and therefore Rosh Chodesh, representing the twelve months, stands mainly for them.
Darkei Moshe ((417: 1, quoting Ohr Zaruah), adds that women, more than men, depend on the timely similar moon cycle, for reaching their body state of conjugal purity. Therefore, Rosh Chodesh that is totally dictated by the moon cycles, is in their zechus and merit.
Rabbi A. Bartfeld as advised By Horav Shlomo Miller and Horav Aharon Miller Shlit’a