Why do Odysseus and his men stay longer than planned on the island of Helios, and what are the consequences of this delay?
In Odyssey 12, Odysseus and his men land on the island of Thrinacia, where the sun god kept a special herd of cattle. Odysseus warned his crew not to harm the sun god’s cattle. Unfortunately, adverse weather conditions prevented Odysseus and his men from leaving the island. The longer they remained on the island, the more dissatisfied Odysseus’ men became with the food that they had. Ultimately, the temptation to kill and eat some of Helios’ cattle became too great and, while Odysseus slept, his men slaughtered and feasted on some of the cattle.
This proved to be deadly mistake. When Helios found out about this, he complained to Zeus. After Odysseus and his men were finally able to leave Thrinacia, Zeus struck their ship with a terrible storm:
“Zeus anchored a black cloud above our hollow ship, and the waves beneath were dark. She had not run on for long before there came a howling gale, a tempest out of the west, and the first squall snapped both our forestays, so that the mast toppled backwards and the rigging fell into the hold, while the tip of the mast hitting the stern struck the steersman’s skull and crushed the bones.”
The ship was destroyed and all of Odysseus’ remaining men died. Odysseus himself managed to float along on remnants of the ship. Eventually, he washed ashore on Calypso’s island.
P.S. The translation in the above answer is from A.S. Kline's translation of the Odyssey.