Changing Eye Color Later in Life. Once a kittenâs eyes have developed completely, by about 3 months of age, his eyes should be done changing color. If, at this point, you detect any other eye color changes, it may be a sign of eye damage or a serious underlying medical condition. Cases in which a catâs eyes change color dramatically over a short period of time are of particular concern. While changing eye color may indicate a relatively common medical concern such as cat eye infection, it may also suggest the presence of more serious, and potentially fatal, ailments.