Since it is a spell with a duration "instantaneous", the spell ends after it is cast and the copy created will remain there. And it says:
It appears to be the same as the original, but it has only one-half of the real creature’s levels or Hit Dice (and the appropriate hit points, feats, skill ranks, and special abilities for a creature of that level or HD).
So I assume there's no hard time limit for how long a simulacrum can stay there after it is created.
Then, let's say a lich somehow falls in love with a human, and that human dies by ageing after half a century. To memorize the lover, this lich creates a simulacrum of its lover. Will this human simulacrum also be affected by ageing later on as the original would, or would it stay as-is forever with the lich?
(I see the creation is considered a construct in 5e, but it seems not the case for 3.5e (it looks like the original's type will be used). It makes sense to be a construct, though. Is the 'copy' from Simulacrum a humanoid or a construct?)
