Why is Navratri celebrated in two different seasons?

Chaitra Navratri, aka Vasanta Navratri, is celebrated in March or April, while Sharad Navratri, aka Maha Navratri, is celebrated in September/October. According to Hindu scriptures, Lord Rama worshipped Goddess Durga before his battle against Ravana, giving rise to Sharad Navratri. Maa Durga later killed demon Mahishasura after a nine-day battle which occurred in Hindu lunar month of Chaitra.