diff --git a/ld_eventsource/http.py b/ld_eventsource/http.py
index 940446a..05c4e3a 100644
--- a/ld_eventsource/http.py
+++ b/ld_eventsource/http.py
@@ -87,7 +87,15 @@ def connect(self, last_event_id: Optional[str]) -> Tuple[Iterator[bytes], Callab
             raise HTTPContentTypeError(content_type or '')
 
         stream = resp.stream(_CHUNK_SIZE)
-        return stream, resp.release_conn
+
+        def close():
+            try:
+                resp.shutdown()
+            except AttributeError:
+                pass
+            resp.release_conn()
+
+        return stream, close
 
     def close(self):
         if self.__should_close_pool: