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.
Paul in the Pokemon fanfic Travels of the Trifecta (yes, THATPaul) spends chapters 3 to 7 suffering from a severe cold/flu and later begins to cough up blood periodically. This is a sign that he has inherited the terminal illness that his mother died from.
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 transferred to a hospital 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 appetite, requiring her to take so many medications to no avail. Ultimately, she was hospitalized and the doctors did all they really could.
In 20XXI, Eirin, due to stress, was starting to become this, developing some anemic condition as a result of stress, but she commits suicide before it becomes an issue
In 20XXII, Keine is revealed to have died of an illness consisting of "pneumonia and lumps in her lungs", Aya dies of heart-attack caused by illness and stress, and Koishi started to become this.
In 20XXIII and later on 20XXIV, after the nukes are dropped, Sakuya dies of radiation sickness.
In 20XXIV, Reimu's mother, Reiko, dies of a long term illness. Earlier, she was ill with radiation sickness before it dissipated.
Reimu (post age-regression) becomes this once again in Gensokyo 20XXV, after living in The Forbiddens for some time, and it was noted that she has been sick off and on.
From 20XXV, we have Yume Ni, in the aftermath of Chen's "The Reason You Suck" Speech. From what is said, she has a chronic illness and later on passed away. Later one, we have Ran, although, unlike the aforementioned Yume Ni, her illness isn't terminal, although it is hindering
From Kill la Kill AU, we have Satsuki, as a result of stress taking a toll on her health. The first time is when she had appendicitis and the second time is when she has Tuberculosis. Later, in comic 41, we have this Ryuuko, after she makes a wish to be the sick one instead of Sats. This is also the subject of a more recent fanfiction where Ryuuko becomes ill and has to be hospitalized for tests. Although, as of chapter 9, it was revealed she had some unknown illness, which turned into septicemia, the which would have and probably could have killed her.
Ruby Rose in the RWBY Henceforward AU was stabbed straight through her spine with Blake Belladonna's Gambol Shroud. Though she narrowly avoids death and paralysis, this inhibits her physical capabilities to an extreme degree. Her reflexes are dulled, she can only lift half her body weight, and she must avoid any more physical trauma if for fear of the damage worsening. This keeps her from achieving her dream of becoming an official huntress and forces her to heavily redesign her weapon and fighting style to manage any sort of combat effectiveness. Funnily enough, though, is she probably worries about her condition the least and still makes a few reckless moves similar to those she would make in her youth (though she has attained a new sort of eerie grace in her fighting that she never had before). Her partner and possible lover, Weiss Schnee, is the one constantly keeping note of Ruby's condition and doing everything she can to make sure Ruby keeps from overdoing it.