[i]If[/i] pulled off correctly, it could be a really heartbreaking story - especially if it continues on after the death of the mortal lover and focuses more deeply on the life and the relationship between the immortal parent and a mortal child. Y'know, that would really be something. It would be a really good setup for the main character's inner war - he (or she) already lost a lover to the tides of time and yet face another big, [i]inevitable[/i] loss. 

I do think it's an older theme - staying alive while everything else withers away; I feel that was pondered on about before, but I may be wrong as well. I know that in Stephen King's Green Mile, for one, that thematic was introduced - watching everyone around you slowly die and everything you know slowly disappear, whilst you remain alive.

But, it's a good question... if I think about it from my perspective, would I walk away or stay with the person - to stay with them may be more caring and kind for the other party involved, but it would probably tear me apart from the inside. Then again, would it really be good for the child if I stayed back, that's the real question. I could very well hold them back in having the normal life, even making them fell sad for my own pain. The pain of me walking away would be sharper, but would last (depending on the age of the other party) shorter than me staying with them until the day of their inevitable death.