diff --git a/gunicorn/asgi/message.py b/gunicorn/asgi/message.py
index 86d97c77..73a6e7da 100644
--- a/gunicorn/asgi/message.py
+++ b/gunicorn/asgi/message.py
@@ -139,7 +139,7 @@ class AsyncRequest:
     async def _parse(self):
         """Parse the request from the unreader."""
         buf = bytearray()
-        await self._read_into(buf, stop=True)
+        await self._read_into(buf)
 
         # Handle proxy protocol if enabled and this is the first request
         mode = self.cfg.proxy_protocol
@@ -174,12 +174,10 @@ class AsyncRequest:
 
         self._set_body_reader()
 
-    async def _read_into(self, buf, stop=False):
+    async def _read_into(self, buf):
         """Read data from unreader and append to bytearray buffer."""
         data = await self.unreader.read()
         if not data:
-            if stop:
-                raise StopIteration()
             raise NoMoreData(bytes(buf))
         buf.extend(data)
 
diff --git a/gunicorn/asgi/protocol.py b/gunicorn/asgi/protocol.py
index 04320986..356bd507 100644
--- a/gunicorn/asgi/protocol.py
+++ b/gunicorn/asgi/protocol.py
@@ -186,9 +186,6 @@ class ASGIProtocol(asyncio.Protocol):
                             peername,
                             self.req_count
                         )
-                except StopIteration:
-                    # No more data, close connection
-                    break
                 except NoMoreData:
                     # Client disconnected
                     break