It should be noted that the quote, "the time for heroes is now dead" comes from the movie version of Beowulf, not the epic poem. The movie's interpretation of the story is much different than the original epic poem.
In the movie, the character Beowulf is flawed and often morally weak. He succumbs to the seductive power of Grendel's mother and then lies to the other characters about it. His relationship with his queen, Welthow, is also damaged by his relationship with a young girl.
The battle with the dragon at the end of the movie, signifies the fact that Beowulf's sins have finally consumed him, although he has still managed to save the Danes from the dragon. Beowulf also notes late in the movie that Christianity has contributed to the killing of monsters and heroes.
The time for heroes is dead because human life has changed. The spread of Christianity, only hinted at in the movie, has transformed human thinking, taking it from superstition to faith. The time for heroes is dead because heroes are no longer needed, at least not in the sense of being saviors.