Regarding the month of October, October 7 is the feast of Our Lady of the Rosary. The Church chose that day and, apparently by extension, the month of October to honor Our Lady of the Rosary because a great victory took place on October 7. In October 1571, the Church in Europe faced a seemingly hopeless challenge. The Muslim Turks had already conquered the Middle East, slaughtering millions and forcing the survivors to convert to Islam. They then moved across the Mediterranean Sea, taking the crucial islands of Crete and Cyprus. From these islands, they set their sights on the Christian kingdoms of the central Mediterranean, threatening Sicily, Venice, and even Rome herself.

As Christians all over Europe prayed for Our Lady’s intercession, the Turks surrounded the Christian ships. But the European fleet broke through. By days’ end, almost all of the Turks were driven to shore or drowned. Europe was saved. Pope Pius established an annual commemoration to honor Our Lady of Victory, and his successor, Gregory XIII, decreed that the first Sunday in October would be the feast of the Holy Rosary.

In summary, the decision to designate October as the month of the Rosary apparently stems from the Church’s desire to extend its thanksgiving to Our Lady for victory in the Battle of Lepanto from one Sunday to a whole month. In addition, when Our Lady appeared in Fatima in May 1917, she identified herself as Our Lady of the Rosary.

SOURCE: https://catholicexchange.com/why-are-may-and-october-months-of-mary