For Odysseus and his men, the loss of Helios, the sun, symbolizes a loss of C. Hope.
In poetry, light ( such as the sun, the moon, candles, stars) often symbolizes good, hope, and freedom.
In the lines "Never the flaming eye of Helios lights on those men at morning, when he climbs the sky of stars, nor in descending earthward out of heaven" the reflected idea is that they do not see the sunrise or sunset anymore, thus they are eventually condemned to a total loss of light, that is to say, hope.
