Why does my arthritis always flare up during my period?

What type of arthri? Menstruation occurs when the female body is at it lowest estrogen and Progesterone levels. So your arthritis may have a hormonal component. Some physicians are using vitamin d for premenstrual syndrome (vitamin d is a hormone and helps prevent breast cancer). Ask your rheumatologist or gynecologist.
Hormones. Clearly the change in hormones causes you to be more aware of your arthritis.