Three days passed away in a blink of an eye.
Originally, Claire planned to return to Triastal right away but as the princess of Camelot asked Azzy to stay for a couple of days more to tour around the kingdom, she was obliged to stay behind for three more days.
As for why Leah asked Azzy to stay around? Naturally, she doesn't want him to treat her place like a training ground. She also wants him to have memories of touring around her kingdom a bit. So far, Azzy has toured only around the city of Camelot, but not the whole kingdom, unlike his foster parents. With so little time for the next semester to start, he decided to enjoy the little time he have with a three-day vacation.