What message does the narrative convey when Axl makes Beatrice promise that she will keep what she has in her heart no matter what?

At the end of the novel, readers face the ultimate truth about couples who grow old together. Even if they have made it through trial and tribulations, at some point, they will have to separate because one will die before the other, leaving the surviving member of the pair the task of going on in life, alone.

When the time comes for Beatrice to cross to the island, she and Axl try to go together. However, in the end, she convinces him to let her go alone. This is ironic as she was the one who expressed concern about the two of them not being able to cross together. Now that she remembers her past, however, her feelings have changed. She knows that her son is dead, so she will not be alone on the island. Also, she no longer feels as close to Axl. Likewise, even though the boatman tells Axl that he'll be back for him, Axl does not seem to care. He keeps on walking without turning back. Perhaps, this is because the realization of what he did in the past gives him a reason to go on, now that the giant is awake. Or, perhaps, it is because he doesn't feel as close to Beatrice now that he knows how she betrayed him. He knows that she is at peace and that was his job. He feels that he will see her again when the time comes, but it is not now. Either way, this love story is a melancholy one.