"A person should make sure to eat before the sixth hour on Shabbos, since it is forbidden to fast on Shabbos". --A column by Daniel Yaakov Travis, citing Talmud Yerushalmi, Taanis 3:11.
On Rosh Chodesh, as well, it's generally forbidden to fast. See, for example, this chapter of Peninei Halachah.
Is Rosh Chodesh like Shabbos in that it's mandatory to eat before solar noon?