diff --git a/httpcore/_async/http11.py b/httpcore/_async/http11.py
index 0493a923d..d484a6250 100644
--- a/httpcore/_async/http11.py
+++ b/httpcore/_async/http11.py
@@ -59,7 +59,7 @@ def __init__(
     ) -> None:
         self._origin = origin
         self._network_stream = stream
-        self._keepalive_expiry: Optional[float] = keepalive_expiry
+        self._keepalive_expiry = keepalive_expiry
         self._expire_at: Optional[float] = None
         self._state = HTTPConnectionState.NEW
         self._state_lock = AsyncLock()
@@ -77,6 +77,16 @@ async def handle_async_request(self, request: Request) -> Response:
             )
 
         async with self._state_lock:
+            # If the HTTP connection is idle but the socket is readable, then the
+            # only valid state is that the socket is about to return b"", indicating
+            # a server-initiated disconnect.
+            server_disconnected = (
+                self._state == HTTPConnectionState.IDLE
+                and self._network_stream.get_extra_info("is_readable")
+            )
+            if server_disconnected:
+                raise ConnectionNotAvailable()
+
             if self._state in (HTTPConnectionState.NEW, HTTPConnectionState.IDLE):
                 self._request_count += 1
                 self._state = HTTPConnectionState.ACTIVE
@@ -280,17 +290,7 @@ def is_available(self) -> bool:
 
     def has_expired(self) -> bool:
         now = time.monotonic()
-        keepalive_expired = self._expire_at is not None and now > self._expire_at
-
-        # If the HTTP connection is idle but the socket is readable, then the
-        # only valid state is that the socket is about to return b"", indicating
-        # a server-initiated disconnect.
-        server_disconnected = (
-            self._state == HTTPConnectionState.IDLE
-            and self._network_stream.get_extra_info("is_readable")
-        )
-
-        return keepalive_expired or server_disconnected
+        return self._expire_at is not None and now > self._expire_at
 
     def is_idle(self) -> bool:
         return self._state == HTTPConnectionState.IDLE
diff --git a/httpcore/_sync/http11.py b/httpcore/_sync/http11.py
index a74ff8e80..f276bdade 100644
--- a/httpcore/_sync/http11.py
+++ b/httpcore/_sync/http11.py
@@ -59,7 +59,7 @@ def __init__(
     ) -> None:
         self._origin = origin
         self._network_stream = stream
-        self._keepalive_expiry: Optional[float] = keepalive_expiry
+        self._keepalive_expiry = keepalive_expiry
         self._expire_at: Optional[float] = None
         self._state = HTTPConnectionState.NEW
         self._state_lock = Lock()
@@ -77,6 +77,16 @@ def handle_request(self, request: Request) -> Response:
             )
 
         with self._state_lock:
+            # If the HTTP connection is idle but the socket is readable, then the
+            # only valid state is that the socket is about to return b"", indicating
+            # a server-initiated disconnect.
+            server_disconnected = (
+                self._state == HTTPConnectionState.IDLE
+                and self._network_stream.get_extra_info("is_readable")
+            )
+            if server_disconnected:
+                raise ConnectionNotAvailable()
+
             if self._state in (HTTPConnectionState.NEW, HTTPConnectionState.IDLE):
                 self._request_count += 1
                 self._state = HTTPConnectionState.ACTIVE
@@ -280,17 +290,7 @@ def is_available(self) -> bool:
 
     def has_expired(self) -> bool:
         now = time.monotonic()
-        keepalive_expired = self._expire_at is not None and now > self._expire_at
-
-        # If the HTTP connection is idle but the socket is readable, then the
-        # only valid state is that the socket is about to return b"", indicating
-        # a server-initiated disconnect.
-        server_disconnected = (
-            self._state == HTTPConnectionState.IDLE
-            and self._network_stream.get_extra_info("is_readable")
-        )
-
-        return keepalive_expired or server_disconnected
+        return self._expire_at is not None and now > self._expire_at
 
     def is_idle(self) -> bool:
         return self._state == HTTPConnectionState.IDLE