as far as I can remember (maybe I am thinking of some other manga which have a similar story), the main guy go back and forth in time because of some power, making him go to one random day of the month each time. This power is given to children born on his birthday day. The main girl also have this power. She dies in one of the first chapters. They try to save her from dying. In the end, to save her, they need to make it as if they never met in the beginning, so the protagonist chose to save her while he loved her.