Why are two days a star sometimes?

Because there are two systems in the perpetual calendar, the first one is twenty-eight nights. Your last one was based on justice drive's calculation and adopted the Taoist method. Which is the traditional almanac algorithm.

The latter is based on Twenty-seven Nights of Manjusri Bodhisattva, and it is the Yaosu Sutra which started in India. The latter algorithm is not popular in Chinese mainland, but the almanac compiled by Mr. Li Juming, a master of Feng Shui in Kong Xuan, mostly adopts the latter algorithm (because Li Juming also studies tantric Buddhism). Because of Mr. Li's international influence, the latter algorithm is now widely circulated.