Why didn't Shannon heal?

Question

Why didn't Shannon in Lost heal from her Asthma when others did? Ben, Locke and Rose's physical disabilities were healed. As shown, several other people were healed as well but not Shannon. Why did the Island impact her differently?

Answer 1

She is not the only one that wasn't healed.

Even excluding people with serious injuries there are several cases of normal healing factor or not healing at all:

• Aaron's (presumably) routine dermatitis. ("Maternity Leave")
• Ben (aka Henry Gale) is wounded by Rousseau in the shoulder on Day By Day 65, in "S.O.S.", Ben’s wound appears better, but not at the same incredible rate that Sawyer was healed from the gunshot. Likewise the injuries inflicted by Sayid also seem to be healing
  normally.
• Charlie's scars surrounding (one under and one over) his left eye. Locke's facial scar over his right eye.
• Locke's stolen kidney does not regenerate. (Its absence saves Locke from dying when Ben shoots him where the kidney would have been.)
• Sawyer's hyperopia (vision problems) and the headaches it causes.
• Shannon's asthma. ("Confidence Man") However, it is worth noting that she only suffered one asthma attack during her time on the Island, which Jack diagnosed as anxiety or panic-induced. Jack mentioned her asthma was worse at that moment, when he was talking to her, because of anxiety. She still suffered from asthma, it just gets worse when she panics. Her breathing improved when Jack helped her calm down, but she was still in the midst of an asthma attack.
• Frank Lapidus is shown to be recovering normally from the injuries sustained in the Ajira Airways Flight 316 crash. ("Namaste"), ("Dead Is Dead")

The reason while the healing properties don't apply to everyone is unknown. You can find some theories here.