Immortal Ovaries

Suppose we have an immortal woman. How long can she remain fertile?

Cecil has said that human ovaries contain the makings of several hundred thousand eggs, but that most “wither away” or “die off” by the time of menopause. So, assuming that in our hypothetical woman, this withering is prevented … how long before there are no eggs left?

I’m figuring at least ten thousand years, but “hundreds of thousands” of eggs is a kind of nebulous number. Any thoughts?