From what I can find (and according to TV Tropes), it is never explained what happened to her father, and it seems to have been more of an excuse to have her end up on the island and get involved in the first place than any real major plot point.
In episode 2, Yukari finds her father and demands to know what had happened. He tells her to calm down, then starts to cry after she tells him that he was the reason she had come there and why she was so upset about not knowing what had happened to him. It is shown in that episode that he knows the Director, who knows that Yukari is his daughter, but it isn't explained why the father left.
The only basic explanation (that I found) was that he went out to look at the moon and never returned.