When you write a story about people, you have written a timeless story. Since people never stop acting the way they do, then a story from 20 years ago reads the same as one written today.
What makes a story dated is technology. It keeps growing and changing, and thus changing how people interact with themselves and the world around them. Romeo & Juliet would not have had any problems if they both had cell phones. But because technology has reached the point where people can communicate instantly from thousands of miles away, the miscommunication angle can't really be justified any more.
The struggle of Romeo & Juliet, though, is timeless. It is true in modern times. It was true for West Side Story. And it was true in Ancient Greece with Pyramus and Thisbe (which the story was a modern retelling of).
This is the value of stories about people. They never get old. They simply become more classic.