First of all, the claim is that pagan myths reflected the cycle of the seasons, with the 'death' of nature in the winter and it's rebirth in the spring.
Probably the best known one to Westerners is the story of Persephone daughter of the goddess of the harvest, Demeter. She was abducted by Hades the king of the underworld and she was taken away to his kingdom. Her mother so grieved her loss that the crops withered and died, and the people began to starve. Zeus went to retrieve Persephone but not before she had eaten six pomegranate seeds. Haven eaten the food of the underworld, Hades said she return to her mother but had to return in six months. So, now every year, the goddess Demeter grieves for six months through Fall and Winter, until her daughter is allowed to return to her in the second half of the year.
Note: Persephone can come and go to the underworld, because she is a living person; she has not died.
Same with Orpheus;
As a living man he journeyed to The Underworld; yet the underworld was not Heaven. In the Underworld, was as it's name suggests, in the Earth and reachable by crossing the river Styx. If a hero or god, was great and beloved, then they could be placed in the Heavens as stars or constellations, but most people descended to the Underworld after death. There they forgot life by drinking from the fountain of forgetfulness.Death of Eurydice
The most famous story in which Orpheus figures is that of his wife Eurydice (also known as Agriope). While walking among her people, the Cicones, in tall grass at her wedding, Eurydice was set upon by a satyr. In her efforts to escape the satyr, Eurydice fell into a nest of vipers and she suffered a fatal bite on her heel. Her body was discovered by Orpheus who, overcome with grief, played such sad and mournful songs that all the nymphs and gods wept. On their advice, Orpheus traveled to the underworld and by his music softened the hearts of Hades and Persephone (he was the only person ever to do so), who agreed to allow Eurydice to return with him to earth on one condition: he should walk in front of her and not look back until they both had reached the upper world. He set off with Eurydice following, and, in his anxiety, as soon as he reached the upper world, he turned to look at her, forgetting that both needed to be in the upper world, and she vanished for the second time, but now forever.
The reason the average living person couldn't cross the Styx, was because the ferryman would only permit the dead into his boat, but it was a fairly material place, with the deceased eating, drinking and interacting. As the legend goes, if the living ate of the food of the dead, they would become part the Underworld.
Only the living could enter and leave the Underworld, yet that is not the same as dying and resurrecting to life.
Later in myths, Orpheus dies a true death, that he doesn't return from and his lyre is placed in the stars in the Heavens.
