Sandglass of Summer Colors (Natsuiro no Sunadokei) is just like this.
At the end of the school year, Makimura Kotaru decides to confess his feelings to Serizawa Kaho. Kaho-chan is considered to be a school idol, and Kotaru gets made fun of, by his friends, telling him he has no chance. But his resolve is set, and Kotaru is determined to reveal his true feelings to the girl he likes.
Afer deciding to write his confession in his letter, he walks home with his childhood friend Senou Ai, who has agreed to give Kaho, a friend of Ai, the letter.
After dropping Ai off at her house, Kotaru observes a suspicous figure and goes to ask this person if they were stalking Ai. Afer wrestling the suspicious person's coat off, it turns out the person's a girl, and Kotaru had accidentally grabbed her chest, during the attempt to wrestle the coat off. She slaps him and breaks an hour glass, sprinkling dust over Kotaru. The girl then runs away.
Feeling ill, Kotaru goes to bed, and wakes up to find that it was somehow the end of summer break, and school was starting again. Confused, he goes to school and finds everyone at the gymnasium. The director was giving a speech about the death of a classmate, Kaho. Kotaru is confused. He finds out that they had been going out all summer too. Kaho had been in a tragic car accident. And he finds out, she was on his way to see him. He faints, and is carried back in time a few times, experiencing his confession to Kaho, and a date they had. Eventually he gets back to his own time, to find this suspicious person from before, standing over him. Her name is Ligene, and is a Time Patroller. Her job is to correct irregularities in time. And she is here to correct time, so that Kaho does not die. It turns out that the dust that Kotaru had been exposed to, gave him the ability to exist out of the framework of time, which would allow him to affect the future.
Ligene tells Kotaru what he must do to prevent the death of his girlfriend. He agrees to do this, because he cannot stand idle. So while going out with Kaho, Kotaru also gives it his all to prevent her death.
Throughout the summer Kaho and Kotaru spend more and more time together. Their bond gets stronger and stronger, and Kotaru is more determined to save Kaho.
Kotaru also discovers that Kaho cares for him very much, and could not bear to be apart from him.
As the fateful day of Kaho's death arrives, everything starts to spiral out of control, and Kotaru finds out he has very little time to save Kaho, if at all. What would he do without his beloved Kaho?
This was a great OVA (non-series) and I recommend anyone, who is a romantic too, to watch this. It's a story that would warm your heart.