It does not matter if the shrine has already received a Golden Rose, as it is seen as a personal gift, given by a specific pope.
Recent popes have been very generous with such awards; Francis is recorded as having given 16 Golden Roses out during his pontificate, while Pope Benedict XVI awarded 19 shrines with a Golden Rose.
Pope Leo XIV asked for the original statue of Our Lady of Fatima to be transferred to the Vatican to allow him to present her another Golden Rose at the recent Marian Jubilee. She presided over the Rosary for Peace held at the Vatican on October 11, which Leo had urged the faithful to join.
The shrine at Our Lady of Fatima has received a total of four Golden Roses.
Brief history of the Golden Rose
According to Fr. William J. Barry in his book, The Sacramentals of the Holy Catholic Church, the gift of the golden rose was originally blessed on Laetare Sunday, the Fourth Sunday of Lent, when the Church briefly anticipates the joy of Easter by wearing rose colored vestments and encourages the congregation to "Rejoice!"
The blessing reflects this joy and calls down God's blessing on those who will receive them.
O Lord, on this day, when the Church exults in Thy name and manifests her joy by this sign [the rose], confer upon us through her true and perfect joy and accepting her devotion of today; do Thou remit sin, strengthen faith, increase piety, protect her in Thy mercy, drive away all things adverse to her and make her ways safe and prosperous, so that Thy Church, as the fruit of good works, may unite in giving forth the perfume of the ointment of that flower sprung from the root of Jesse and which is the mystical flower of the field and lily of the valleys, and remain happy without end in eternal glory together with all the saints.
Originally these roses were sent to kings, queens, princesses and princes. It was a gesture that was rich in symbolism, as Fr. Barry explains in his book.
The papal gift reminds its royal recipient that the lustre of his virtue ought to be like the glitter of gold among metals and the brilliancy of the rose among flowers. Balsam, mixed with musk, is poured over the Golden Rose to teach the sovereign that his lofty station requires him to spread abroad the sweet odor of royal virtue, and that, like balm, he ought to heal up the wounds of the State, and, as it does for material bodies, preserve the political body from corruption.
The last royal leader to receive it was Charlotte, Grand Duchess of Luxembourg. Since the pontificate of Pope Paul VI, each pope has given the gift as a special honor to various Marian shrines across the world, honoring the Queen of Heaven.