It would be unlikely that you’d totally lose your period from fasts if your overall nutrition is meeting your needs.
That said, fasting can absolutely mess up your cycle. I’ve had periods be significantly late, and once I started my period two weeks early from fasting. Fasting affects your hormones and thus your menstrual cycle.
I experienced the opposite. I have had irregular menstruation cycles since I was a teen. Last year, I believe I only had my period 3 times. When I started fasting in February, I immediately got my period in the same week and just finished another cycle this month.