I did some searching and came up with a lot of sources saying, stuff similar to the following.
"If you are using steroids in high dosages, you could have problems related to your menstrual cycle. This drug can interfere with your period and cause you to have irregular periods, especially after prolonged use. Aside from the irregularity in your menstrual cycle, you might not have a period at all. In addition, some women experience heavy bleeding, severe abdominal cramps, upset stomach, and more while using the drug."
Prednisone is a synthetic version of Cortisol, which is a natural hormone in your body. You're basically flooding your body with higher levels of cortisol than your body could naturally produce. Hormones can mess with other processes in the body, here is an example I saw stated a few times:
"Stress activates a hormonal pathway in the body called the hypothalamic-pituitary-adrenal (HPA) axis (10). Activation of HPA axis is associated with increased levels of cortisol and corticotropin-releasing hormone (CRH) (2, 10, 11). The HPA axis, cortisol, and CRH help control stress response in the body. CRH and cortisol release can suppress normal levels of reproductive hormones, potentially leading to abnormal ovulation, anovulation (i.e. no ovulation), or amenorrhea (i.e. absence of menstruation) (10–12). "
Sounds like prednisone can mess with your natural cycle in all sorts of ways..