The question if one can have a fit immune system and still be ill sometimes, is an interesting one. The answer turns out to be confirmative, which can be illustrated by the example of a cold. The symptoms of a cold are caused by an immune reaction to a virus intruding the body. The purpose of this immune reaction is to destroy the virus and the symptoms belonging to this reaction of the immune system are telling you that your immune system is functioning normal.
Immune reactions are also called inflammatory reactions. In the case of a cold there is an inflammation of the nasal mucous membrane, which is known as rhinitis. White blood cells enter the tissue that is infected by the virus and destroy them. Often collateral damage to the tissue is caused, which can lead to certain symptoms of illness. Most of the times immune reactions are a succes: intruders are destroyed and tissue is repaired, and the patient is fully recovered. But indeed one can become ill because of a normally functioning immune system, during the phase of destroying micro organisms such as viruses or bacteria.