Toki wo Kakeru Shoujo, Higashi no Eden Recommendations
When one is given the ability to live frivolously, their entire life is put in perspective.
Both centre around the theme of being granted something precious but expendable, and the morality and choices behind how to use this thing. Both great shows with a sense of mystery.
I agree with the original recomender on this one. The two have a very similar air about them and chances are if you like one you will probably enjoy the other.