diff --git a/httpcore/_async/http11.py b/httpcore/_async/http11.py
index 5d6ee440..d484a625 100644
--- a/httpcore/_async/http11.py
+++ b/httpcore/_async/http11.py
@@ -68,8 +68,6 @@ def __init__(
             our_role=h11.CLIENT,
             max_incomplete_event_size=self.MAX_INCOMPLETE_EVENT_SIZE,
         )
-        # Assuming we were just connected
-        self._network_stream_used_at = time.monotonic()
 
     async def handle_async_request(self, request: Request) -> Response:
         if not self.can_handle_request(request.url.origin):
@@ -185,7 +183,6 @@ async def _send_event(
         bytes_to_send = self._h11_state.send(event)
         if bytes_to_send is not None:
             await self._network_stream.write(bytes_to_send, timeout=timeout)
-            self._network_stream_used_at = time.monotonic()
 
     # Receiving the response...
 
@@ -237,7 +234,6 @@ async def _receive_event(
                 data = await self._network_stream.read(
                     self.READ_NUM_BYTES, timeout=timeout
                 )
-                self._network_stream_used_at = time.monotonic()
 
                 # If we feed this case through h11 we'll raise an exception like:
                 #
diff --git a/httpcore/_sync/http11.py b/httpcore/_sync/http11.py
index 33342fb6..f276bdad 100644
--- a/httpcore/_sync/http11.py
+++ b/httpcore/_sync/http11.py
@@ -68,8 +68,6 @@ def __init__(
             our_role=h11.CLIENT,
             max_incomplete_event_size=self.MAX_INCOMPLETE_EVENT_SIZE,
         )
-        # Assuming we were just connected
-        self._network_stream_used_at = time.monotonic()
 
     def handle_request(self, request: Request) -> Response:
         if not self.can_handle_request(request.url.origin):
@@ -185,7 +183,6 @@ def _send_event(
         bytes_to_send = self._h11_state.send(event)
         if bytes_to_send is not None:
             self._network_stream.write(bytes_to_send, timeout=timeout)
-            self._network_stream_used_at = time.monotonic()
 
     # Receiving the response...
 
@@ -237,7 +234,6 @@ def _receive_event(
                 data = self._network_stream.read(
                     self.READ_NUM_BYTES, timeout=timeout
                 )
-                self._network_stream_used_at = time.monotonic()
 
                 # If we feed this case through h11 we'll raise an exception like:
                 #