He did die, though do not all living things die? I hope you don't have a problem with death -that would be tough.
At best, Beowulf died after having living a full and adventurous life. Beowulf defeated the monstrous Grendel and Grendel's mother, saving Herot. Rewarded for his heroics, Beowulf also presided as a good and generous king over Geatland for 50 years. He did later die of his wounds in his battle with the Dragon that terrorized Geatland. Ultimately Beowulf defeated the dragon in his last adventure with the sole aid of his loyal friend Wiglaf.
A great warrior, a good king, and an honored man.