This is true, ArM5, p. 105. "[familiars] only suffers ill effects from aging when the magus does". Disadvantage (from the animal's point of view) is that the familiars dies when the magus dies, even if the unbound animal is potentially immortal.
As long as the campaign lasts, or until its age seems like a good sub-plot.
For the answer to questions like this, look to books and movies you like. How many stop the main plot because a character (human or non-) is "getting too old for this"? A few, and then those tend to be about that character and their age as a focus.
If it makes a good story, go with it. If not, don't worry about it - there's ample room to have fae/magical creatures live as long as any mage, and more.
Magical creatures do not age; in common with many things from the Magic Realm, change comes very hard to them. Instead, they suffer Acclimation, which is an accretion of their magic due to contact with the mundane. RoP:M, chapter 4 has more details.
Faeries have bodies that are made of glamour animated by vitality, so they don't suffer ageing either (RoP:F, chapter 3). However, they sometimes gradually change as years pass, as they become subject to different mortal forces altering their stories.
Both groups can have Flaws which cause the effects of ageing.
Familiars who are members of the Magic or Faerie Realms are bound to a human, and inherit ageing through that bond, as someone has already pointed out. Whilst not specifically addressed in the RoP books, this is probably due to the close magical bond that joins them. Familiars are safe from Acclimation thanks to the Familiar Bond.