She thinks Odysseus will forget about his home and family and stay with her.
17 days
Calypso offers immortality to Odysseus
She offers Odysseus immortality.
In the Odyssey, Odysseus stays on the Calypso's island of Ogygia for 7 years. Other accounts say 5 years, while the story by Hyginus states one.He also spent a year on Circe's island Aeaea.
Odysseus stays with Calypso [The Hider] on Ogygia for seven years.
Money
He is the sun god, his island is Thrinacia on which Odysseus' men eat Hyperion's sacred cattle. This causes Hyperion to ask Zeus to shipwreck Odysseus, and so he is washed up on Calypso's island, where he stays for 7 years.
He stays so long because of her sexual seduction and he has not ship to leave on and Calypso will not help build him a ship. Until Zeus convinces her to allow him to leave that is when she supplies Odysseus with thing to make a raft but she doesn't help him build it.
Odysseus stays on Circe's island for one year.In a movie version, he stays for what seems like 7 days, but is in reality 7 years.
In "The Blood of Olympus," Calypso stays on her island while Leo leaves to help the Greek demigods in their battle against Gaea. After the battle, Leo sacrifices himself to save his friends and is presumed dead, but he is later revealed to be alive and well with Calypso on her island. They are happy together and remain there studying and practicing their skills.
Circe is a sorceress, she enchants Odysseus and turns men into pigs, although she doesn't do this to Odysseus (lucky man) she does it to his remaining soldiers. So it is the enchantment that keeps him on the island,
When he wants to listen to the siren's song. When he stays on the cyclop's island just to know what the beast looked like.