In the "Tolkein"iverse, this was somewhat addressed - if you were an elf, your life had no specific bound; if you were a man / dwarf, age affected you.
Of course, Tolkein didn't balance his characters -- elves were generally stonger, faster, prettier, and smarter, lacking only (if anything) a desire to fill continents with their kind. Since an RPG needs more balance, you could restrict elven or similar characters to grow much more slowly, i.e. take much longer to reach normal levels of strength / wisdom, what have you, but the character never weakens.
Also, with human (read "mortal") characters, I don't see death of old age as a good idea - just start dropping the strength and agility after some point, stopping at some point that is weaker than youth, but not crippling. Then you become a wise old man who relies on magic or alliances to fight. The basic idea is that if you like fighting with your fists, you need to play a series of young mortal characters if you are a mortal.
Of course we could decouple the human/elf distinction from the mortal / immortal distinction - if you want to be immortal, you would start with 1/3 of the stats of a mortal, regardless of race, and build stats more slowly, maybe. We've drifted from strict Tolkein, and some drift is inevitable in a game setting.
It also seems like immortals would necessarily have a longer adolescence. So wisdom should grow slowly and the max be connected to age, esp. for immorts?
If old age is going to be in the cards, I imagine it being something like 2-5 years real time for it to take hold. Arguably the death realm could be different for mort. vs. immort and possibly mortals paying some kind of aging penalty for dying - maybe it takes the equivalent of 2 days of real time off your stay in Yliakum?
Sorry if some of this has been discussed - I took everything I was going to write, and removed

all the stuff that wasn't weird enough (this is advice for life - remove everything that isn't weird enough

.)
Sw.