Desperation (Absence)
Mamoru Kodate, Kenji Kondo, and Sakura Kaname are among the candidates to pilot the Fafners. Meanwhile, Kazuki and Yukie are questioning the reason of their imprisonment. As a new Festum approaches, the new pilots are soon tested to defeat it. Mamoru devises a plan, ignoring Soushi's specified orders. The three collaboratively succeed in defeating the Festum, yet they are put in confinement for acting on their own judgment. Soushi learns from Fumihiko that Kazuki denies himself daily, bypassing any assimilation. Maya realizes that Soushi has feelings for Kazuki. Michio brings Kazuki to the deck of the ship, also encountering Canon, before arriving at the Moldova base.
Aired 26/09/2004EP 12 - Desperation (Absence)

Fafner
Tatsumiyajima is the central island in the middle of a small cluster of islands, in a sleepy backwater of the Japanese isles. Not much happens there, and the island's young people go to school knowing that their lives are likely to remain peaceful and undisturbed. Or so they have been taught... but the truth is different. The fate of mankind is on the line, and Tatsumiyajima is the last line of defense against a hostile and incomprehensible enemy. At the center of it all, fighting for Humanity's continued existence, is the giant robot Fafner, the dragon that guards this final treasure of mankind.
(Source: Anime News Network)
Note: The last episode aired with a runtime of ~48 minutes as opposed to the standard 24 minute long episode. In the DVD release and subsequent home video releases of the series, the final episode was split into two separate ~24 minute long episodes.