There is said to be hope for a sick man, as long as there is life.

[Aegroto dum anima est, spes esse dicitur.]

Marcus Tullius Cicero (106-43 BC) Roman orator, statesman, philosopher

Epistulae ad Atticum [Letters to Atticus], Book 9, Letter 10 (9.10), sec. 3, l. 19 (18 Mar 49 BC) [tr. Shackleton Bailey (1968)]
    (Source)

Alt. trans.: "A sick man is said to have hope, so long as he has breath." [tr. Winstedt (1913)]

Often paraphrased as: "While there is life there is hope" [Dum anima est, spes est.] See also Theocritus, "While there's life there’s hope, and only the dead have none" (Idyll #4, l. 42 [tr. Gow]).