When does a broken pipe occur in a TCP stream?

I am trying to write an echo server in Rust.

use std::net::{TcpStream, TcpListener};
use std::io::prelude::*;

fn main() {
    let listener = TcpListener::bind("0.0.0.0:8000").unwrap();
    for stream in listener.incoming() {
        let stream = stream.unwrap();
        println!("A connection established");
        handle_connection(stream);
    }

}

fn handle_connection(mut stream: TcpStream) {
    let mut buffer = [0; 512];

    stream.read(&mut buffer).unwrap();

    println!("Request: {}", String::from_utf8_lossy(&buffer[..]));
    stream.write(&buffer[..]).unwrap();
    stream.flush().unwrap();
}

The first request with nc localhost 8000 is working as expected but subsequent request aren't. What am I doing wrong? Is the problem in how the server is reading requests from clients? Though there is no error server side.

I am sending data by typing them on the terminal:

$ nc localhost 8000
hi
hi
hello
# no response
# on pressing enter
Ncat: Broken pipe.