There's no real answer out there in cannon, so all I can tell you is how I've worked it.
For wizards and sorcerers, once the familiar reaches adulthood, they age with their master--so they do get age categorized to the point at which their master is.
So if a mage is old, and they get, say a rat or snake, the rat or snake will reach adulthood, and the progress to the age category of the master, but will not die unless they are killed, or their master dies.
You can work it the opposite way as well--if the master is young or very young, the rat may stay closer to teen/adult for longer.
My rule of thumb has been to have them age naturally until maturity though, and then simply grow with their master.
I don't apply this to druids or to rangers though. My reasoning is that those characters are closer to the life/death cycle of the earth, and are more naturalistic. But, that being said, you can certainly do the same as I have for mage-types.
Here's my reasoning on the familiar aging for wizards & sorcerers:
- they BECOME magical beasts when they gain the status of familiars
- many stats are tied to the status of the master of the familiar, so it follows that age category and longevity might be as well. These are not ordinary to their species.
Hit Dice: For the purpose of effects related to number of Hit Dice,
use the master’s character level or the familiar’s normal HD total,
whichever is higher.
Hit Points: The familiar has one-half the master’s total hit points
(not including temporary hit points), rounded down, regardless of its
actual Hit Dice.
Attacks: Use the master’s base attack bonus, as calculated from all
his classes. Use the familiar’s Dexterity or Strength modifier,
whichever is greater, to get the familiar’s melee attack bonus with
natural weapons.
Skills: For each skill in which either the master or the familiar has
ranks, use either the normal skill ranks for an animal of that type or
the master’s skill ranks, whichever are better. In either case, the
familiar uses its own ability modifiers. Regardless of a familiar’s
total skill modifiers, some skills may remain beyond the familiar’s
ability to use.
Familiar Ability Descriptions: All familiars have special abilities
(or impart abilities to their masters) depending on the master’s
combined level in classes that grant familiars.