diff --git a/src/mcp/client/session.py b/src/mcp/client/session.py
index 0cea454a77..4b8f73efe0 100644
--- a/src/mcp/client/session.py
+++ b/src/mcp/client/session.py
@@ -57,6 +57,8 @@ async def __call__(
 async def _default_message_handler(
     message: RequestResponder[types.ServerRequest, types.ClientResult] | types.ServerNotification | Exception,
 ) -> None:
+    if isinstance(message, Exception):
+        raise message
     await anyio.lowlevel.checkpoint()
 
 
diff --git a/src/mcp/shared/session.py b/src/mcp/shared/session.py
index 243eef5ae6..2cfd363ab2 100644
--- a/src/mcp/shared/session.py
+++ b/src/mcp/shared/session.py
@@ -440,7 +440,7 @@ async def _handle_session_message(message: SessionMessage) -> None:
             except Exception as e:
                 # Other exceptions are not expected and should be logged. We purposefully
                 # catch all exceptions here to avoid crashing the server.
-                logging.exception(f"Unhandled exception in receive loop: {e}")  # pragma: no cover
+                logging.exception(f"Unhandled exception in receive loop: {e}")
             finally:
                 # after the read stream is closed, we need to send errors
                 # to any pending requests
@@ -516,7 +516,9 @@ async def _handle_response(self, message: SessionMessage) -> None:
         if stream:
             await stream.send(message.message)
         else:
-            await self._handle_incoming(RuntimeError(f"Received response with an unknown request ID: {message}"))
+            logging.warning(
+                "Received response with unknown request ID %r — dropping (request may have timed out)", response_id
+            )
 
     async def _received_request(self, responder: RequestResponder[ReceiveRequestT, SendResultT]) -> None:
         """Can be overridden by subclasses to handle a request without needing to
diff --git a/tests/issues/test_1401_client_session_error_handling.py b/tests/issues/test_1401_client_session_error_handling.py
new file mode 100644
index 0000000000..35fbe3b3fa
--- /dev/null
+++ b/tests/issues/test_1401_client_session_error_handling.py
@@ -0,0 +1,132 @@
+"""Tests for issue #1401: ClientSession should propagate transport exceptions.
+
+Root cause: _default_message_handler called anyio.checkpoint() unconditionally,
+silently dropping exceptions. The async-for loop in _receive_loop then called
+`continue`, waiting for the next message that never came — hanging all pending
+requests indefinitely.
+
+Fix: _default_message_handler re-raises when the message is an Exception
+(transport errors from the stream). This propagates out of _receive_loop's
+async-for, triggering the finally block that closes all pending response streams
+with CONNECTION_CLOSED — unblocking any in-flight callers.
+
+Protocol-level non-fatal errors (e.g. responses with unknown request IDs from
+timed-out requests) are handled inline in _handle_response with a warning log,
+so they do not reach _default_message_handler and cannot kill the session.
+"""
+
+import anyio
+import pytest
+from anyio.abc import TaskStatus
+
+from mcp import types
+from mcp.client.session import ClientSession, _default_message_handler
+from mcp.server import Server, ServerRequestContext
+from mcp.shared.exceptions import MCPError
+from mcp.shared.message import SessionMessage
+from mcp.types import CallToolRequestParams, CallToolResult, TextContent
+
+
+@pytest.mark.anyio
+async def test_default_message_handler_raises_on_exception():
+    """_default_message_handler must re-raise Exception instances."""
+    err = RuntimeError("transport failure")
+    with pytest.raises(RuntimeError, match="transport failure"):
+        await _default_message_handler(err)
+
+
+@pytest.mark.anyio
+async def test_default_message_handler_checkpoints_on_notification():
+    """_default_message_handler should checkpoint (not raise) for non-exception messages."""
+    notification = types.ToolListChangedNotification(method="notifications/tools/list_changed")
+    # Should complete without raising
+    await _default_message_handler(notification)
+
+
+@pytest.mark.anyio
+async def test_transport_exception_unblocks_pending_request():
+    """A transport exception must unblock pending requests instead of hanging them.
+
+    Before the fix: exception was swallowed by checkpoint(); async-for looped
+    back waiting for the next message; pending call_tool hung indefinitely.
+
+    After the fix: exception propagates out of the async-for, _receive_loop's
+    finally block closes all pending response streams with CONNECTION_CLOSED,
+    and call_tool raises MCPError rather than hanging.
+    """
+    slow_tool_started = anyio.Event()
+
+    async def handle_call_tool(ctx: ServerRequestContext, params: CallToolRequestParams) -> CallToolResult:
+        slow_tool_started.set()
+        await anyio.sleep(60)  # hangs until cancelled
+        return CallToolResult(content=[TextContent(type="text", text="never")])  # pragma: no cover
+
+    server = Server(
+        name="test",
+        on_call_tool=handle_call_tool,
+    )
+
+    server_writer, server_reader = anyio.create_memory_object_stream[SessionMessage](4)
+    client_writer, client_reader = anyio.create_memory_object_stream[SessionMessage | Exception](4)
+
+    call_tool_error: Exception | None = None
+    server_scope: anyio.CancelScope | None = None
+
+    async def run_server(*, task_status: TaskStatus[anyio.CancelScope]) -> None:
+        with anyio.CancelScope() as scope:
+            task_status.started(scope)
+            await server.run(server_reader, client_writer, server.create_initialization_options())
+
+    async def run_client() -> None:
+        nonlocal call_tool_error
+        async with ClientSession(client_reader, server_writer) as session:  # type: ignore[arg-type]
+            await session.initialize()
+
+            async def inject() -> None:
+                await slow_tool_started.wait()
+                # Inject a transport exception — simulates e.g. httpx.ReadTimeout
+                await client_writer.send(RuntimeError("sse read timeout"))
+
+            async with anyio.create_task_group() as tg:
+                tg.start_soon(inject)
+                try:
+                    await session.call_tool("slow")
+                except (MCPError, RuntimeError) as e:
+                    call_tool_error = e
+                    tg.cancel_scope.cancel()
+
+        assert server_scope is not None
+        server_scope.cancel()
+
+    async with anyio.create_task_group() as tg:
+        server_scope = await tg.start(run_server)
+        tg.start_soon(run_client)
+
+    assert call_tool_error is not None, "call_tool should have raised, not hung"
+
+
+@pytest.mark.anyio
+async def test_custom_message_handler_receives_exception():
+    """A custom message_handler can intercept transport exceptions without re-raising."""
+    received: list[Exception] = []
+
+    async def capturing_handler(message: object) -> None:
+        if isinstance(message, Exception):  # pragma: lax no cover
+            received.append(message)  # capture — do not re-raise
+
+    server_writer, server_reader = anyio.create_memory_object_stream[SessionMessage](4)
+    client_writer, client_reader = anyio.create_memory_object_stream[SessionMessage | Exception](4)
+
+    async with server_reader, server_writer:
+        async with ClientSession(
+            client_reader,  # type: ignore[arg-type]
+            server_writer.clone(),
+            message_handler=capturing_handler,
+        ):
+            await client_writer.send(ValueError("custom handler test"))
+            await client_writer.aclose()
+            await anyio.sleep(0.05)
+
+    assert len(received) == 1
+    assert isinstance(received[0], ValueError)
+    assert str(received[0]) == "custom handler test"