While she uses Sakuya's World, she can keep moving, therefore her biological functions resume. This includes cell division, which has a limit (the Hayflick limit, based on the length of the telomeres at the ends of the DNA-strands). Once the limit is reached, the next division would likely result in errors, so the cell self-destructs.
Since her personal time keeps moving while the world stands still, she would appear to be aging faster than normal, and provided Gensoukyou obeys conventional biology, she would die of old age sooner than her calendar age would indicate.
ThunderBird said: Stuff about the limit of cell division
Just out of curiosity, what would happend if she were to die inside her "sakuya's world" spell? would the time freeze forever or would it return to normal after her death?
One of the game ending has Remilia stating she can't remember how long Sakuya has been working for her.
If she were mortal a 500+ year old vampire should be able to remember a scant 10-20 years(even less if she were able to age during time stops). Chances are she's already immortal by one means or another.
Even barring all that if you consider the series' overall emphasis on immortality, agelessness and eternity in general any character aging or dying(and not returning as undead) is unlikely.
