Jinki:Extend

Akao Hiiragi lives in Japan, and she has lost her entire memory except for three years ago. But one day she meets a mysterious man named Ryouhei who tells her that she is a "cognate;" a person with special powers that enable them to pilot robots called Jinki. All across the world, a mysterious phenomenon is occurring, known as the "Lost Life Phenomenon," where an entire town is destroyed from a series of mysterious nuclear-like explosions. Akao discovers that this is not a natural phenomenon, and that it is being caused by a mysterious and evil group called the Hachishoujin, who are also cognates, and pilot their own Jinkis. Even though she hates to fight, Akao must pilot a Jinki to protect the ones she loves.

(Source: ANN) Jinki:Extend had three volumes published in English by ADV Manga from July 27, 2004 to November 23, 2004 before the license was dropped and the publisher went defunct.