Out of curiosity, I looked up the definition of illness. Seems to be so loosely defined that it can be either a disease or a patient's personal experience, including "lethargy, depression, loss of appetite, sleepiness, hyperalgesia, and inability to concentrate", which (possibly excluding hyperalgesia, I've not heard of that before now) are associated with aging.

Regardless of if "illness" is or is not a terminological inexactitude, it looks like ageing is a chronic progressive terminal genetic disorder. I think "cure" is an appropriate term in this case.