Lance Wabisuke-Hamilton from One Piece: Parallel Works has a mysterious illness that causes him to fall asleep at random times and makes him physically weak. However, Word of God states that Lance's condition is not life-threatening.
In the Touhou Project fanfiction Reimu's Illness, because of her unstable (it is described as being up and down) health, Reimu falls ill with tuberculosis, human enterovirus 68, and viral meningitis and she is so sick that she's had to be transfered to a hopsital in the city and be placed in something called an isolation box (which is akin to an incubator for premature infants).
In Gensokyo 20XX, she has been plagued with colds, depression, and various other ailments, even lack of sleep and appatite, requiring her to take so many medications to no avail. Ultimately, she was hospitalized and the doctors did all they really could.