Would a girl abandon the young man her family approved of and who pledged to marry her, after he suffered successive health problems, believing that she is an "ill omen" for him?

If the suitor is a man of good character and religious commitment, it is preferable to wait and be patient with him until he overcomes his ordeal. If he withdraws from the engagement, it might be better for you, as one does not know where goodness lies. Allah Almighty says: "But perhaps you hate a thing and it is good for you; and perhaps you love a thing and it is bad for you. And Allah Knows, while you know not." (Al-Baqarah: 216). Your statement that destiny is against you is wrong, for all the affairs of a believer are good. However, if the reason for his withdrawal is pessimism and divination, then this is not permissible for him, as divination is forbidden in Islam. The suitor is a non-mahram, and it is not permissible for you to be in seclusion with him or to establish a romantic relationship with him.