Is it established anywhere how old Mrs. Norris is?
Reading this answer about the Marauders' Map made me wonder how old Filch's cat is at the time of the books. Granted, it seems Mrs. Norris was well cared for and it's possible she may have had some magical intervention to help prolong her life (e.g. we know she was eventually healed (for lack of a better term) after the reflected basilisk gaze petrified her), but it seems she has likely had an extraordinarily long life for a house cat.
If James and his buddies made the map while they were at Hogwarts and made a point of tracking the cat, then she would have to be at least 16 years old when Harry received the map. If the speculation in that answer is correct, it seems likely the kitty is significantly older, as she would have annoyed the Marauders enough to get them to have the map track her. While cats have been known to live to be more than 30 years old, 16 or 17 is pretty old, even for well cared for house cats.