What reason does Victor give for why he did not die during his illness in prison in Frankenstein?

His reason was that; he was doomed to live until he fulfills his destiny.

Explanation:

Victor was accused of the murder of Henry Clerval by his townspeople. The sight of Clerval's dead body made him to suffer delirium of fever and convulsion.

He was terribly sick for some time and wished for death, but unfortunately death never came for him. This made him to realize that he was doomed to be alive.

He was visited by his dad at the prison, discharged and acquainted by Mr. Kirwin, the town magistrate. He got married to Elizabeth who was killed at the night of their wedding by a monster.