diff --git a/cli/src/mpftp/sidecar.py b/cli/src/mpftp/sidecar.py
index c50dfb3..459fa9e 100644
--- a/cli/src/mpftp/sidecar.py
+++ b/cli/src/mpftp/sidecar.py
@@ -1159,7 +1159,10 @@ def _network_open_error(self, device: str, exc: BaseException) -> str:
         answers ping (lwIP has its own task), but WebREPL never replies, since
         the esp32 port only services its sockets from the VM's poll hook. So a
         silent WebREPL on a host that answers ping, or on a board that logged
-        in earlier in this session, is a busy board, and the user is told so.
+        in earlier, is a busy board, and the user is told so. When the TCP
+        connect itself timed out, though, the board may simply be off: then
+        ping decides even for a board that answered before, so a switched-off
+        board isn't sent to serial or the reset button.
         """
         text = str(exc)
         if isinstance(exc, webrepl.WebReplAuthError):
@@ -1172,7 +1175,9 @@ def _network_open_error(self, device: str, exc: BaseException) -> str:
         )
         if not silent:
             return text
-        if "never answered the WebSocket upgrade" in text or device in self._answered:
+        if "never answered the WebSocket upgrade" in text:
+            return f"{device}: {wifiboard.STUCK_MESSAGE}"
+        if device in self._answered and "no answer from" not in text:
             return f"{device}: {wifiboard.STUCK_MESSAGE}"
         try:
             host = webrepl.parse_device(device)[0]
diff --git a/cli/tests/test_wifi_access.py b/cli/tests/test_wifi_access.py
index 1980724..036921a 100644
--- a/cli/tests/test_wifi_access.py
+++ b/cli/tests/test_wifi_access.py
@@ -375,14 +375,31 @@ def test_a_host_that_is_gone_keeps_the_plain_message(self):
         with mock.patch.object(webrepl, "host_answers_ping", return_value=False):
             self.assertEqual(s._network_open_error("ws://10.0.0.5", err), str(err))
 
-    def test_a_board_that_answered_before_is_busy_without_asking_ping(self):
+    def test_a_board_that_answered_before_and_goes_quiet_after_connecting_is_busy(self):
         s = sidecar.Session()
         s._answered.add("ws://10.0.0.5")
-        err = webrepl.WebReplError("ws://10.0.0.5: no answer from 10.0.0.5:8266 in 5 s.")
+        err = webrepl.WebReplError("ws://10.0.0.5: no the password prompt within 5 s (got b'')")
         with mock.patch.object(webrepl, "host_answers_ping") as ping:
             self.assertIn(wifiboard.STUCK_MESSAGE, s._network_open_error("ws://10.0.0.5", err))
         ping.assert_not_called()
 
+    def test_a_board_that_answered_before_and_is_now_off_is_not_called_busy(self):
+        # A saved board that's switched off: the TCP connect times out and
+        # ping gets no answer, so the plain "is the board on this network"
+        # message stands.
+        s = sidecar.Session()
+        s._answered.add("ws://10.0.0.5")
+        err = webrepl.WebReplError("ws://10.0.0.5: no answer from 10.0.0.5:8266 in 5 s.")
+        with mock.patch.object(webrepl, "host_answers_ping", return_value=False):
+            self.assertEqual(s._network_open_error("ws://10.0.0.5", err), str(err))
+
+    def test_a_board_that_answered_before_and_still_answers_ping_is_busy(self):
+        s = sidecar.Session()
+        s._answered.add("ws://10.0.0.5")
+        err = webrepl.WebReplError("ws://10.0.0.5: no answer from 10.0.0.5:8266 in 5 s.")
+        with mock.patch.object(webrepl, "host_answers_ping", return_value=True):
+            self.assertIn(wifiboard.STUCK_MESSAGE, s._network_open_error("ws://10.0.0.5", err))
+
     def test_a_refused_connection_is_not_called_busy(self):
         s = sidecar.Session()
         s._answered.add("ws://10.0.0.5")