Why?

Madeleine watched as the two geniuses charged toward her with an unconcealed disappointment in her eyes. One of the reasons she so very much cherished the time she had spent with Dyon was because he taught her to fight, something she had forgotten when she fell ill.

The reason Madeleine chose to marry Akihiko after she thought Dyon died wasn't because she was too cowardly to commit suicide. In fact, it took everything within her to fight back the impulse, to not give up, to always look for a path to live.

Madeleine wanted Dyon's name to be remembered. She wanted the things he had done for her, the sacrifices he had made, to live on. If she had given up and died, what would Dyon's death have meant? Would anyone have spoken of him anymore? Would he still be remembered?

In the end, it was because of this will to live, to fight on, that Madeleine was alive when Dyon finally came back. Wouldn't it have been far too tragic if she hadn't been?