Toki wo Kakeru Shoujo - Tokikake

After 17 ordinary years on Earth, Makoto Konno's journey was about to be ended by a freak accident. Then, life gave her a reset button. With her new found time-leaping powers, she immediately sets out to wipe off all the little annoyances in her daily life, from failing grades to iffy relationships she can't handle. But as her time-leaps get more frequent, she is forced to realize that every change she makes has profound repercussions that she can't foresee...and should her powers fail her, the consequences could be disastrous...

This was set as a prelude to the 2006 animated film of the same title, which was in turn loosely based on the 1965 novel.