diff --git a/port_forwarder.go b/port_forwarder.go
index 1351025cb..f47d11565 100644
--- a/port_forwarder.go
+++ b/port_forwarder.go
@@ -123,13 +123,28 @@ func (fwd *PortForwarder) handleConnection(ctx context.Context, id channelID, co
 	}()
 
 	// Bi-directional copy of data.
-	// If any individual connection has an error, we can safely ignore them
-	// and defer to connection clients to handle data loss as necessary.
-	go io.Copy(conn, channel)
-	go io.Copy(channel, conn)
+	errs := make(chan error, 2)
+	copyConn := func(w io.Writer, r io.Reader) {
+		_, err := io.Copy(w, r)
+		errs <- err
+	}
+	go copyConn(conn, channel)
+	go copyConn(channel, conn)
 
-	<-ctx.Done()
-	return ctx.Err()
+	// wait until context is cancelled or we've received two io.EOF
+Loop:
+	for i := 0; i < 2; i++ {
+		select {
+		case <-ctx.Done():
+			return ctx.Err()
+		case err := <-errs:
+			if err != nil && err != io.EOF {
+				break Loop // non-EOF errors stop connection handling
+			}
+		}
+	}
+
+	return nil
 }
 
 // safeClose reports the error (to *err) from closing the stream only