diff --git a/src/engineio/async_client.py b/src/engineio/async_client.py
index 238ba52..2820265 100644
--- a/src/engineio/async_client.py
+++ b/src/engineio/async_client.py
@@ -571,7 +571,7 @@ async def _read_loop_polling(self):
 
     async def _read_loop_websocket(self):
         """Read packets from the Engine.IO WebSocket connection."""
-        while self.state == 'connected':
+        while self.state == 'connected' and self.write_loop_task:
             p = None
             try:
                 p = await asyncio.wait_for(
@@ -672,7 +672,6 @@ async def _write_loop(self):
                 if r.status < 200 or r.status >= 300:
                     self.logger.warning('Unexpected status code %s in server '
                                         'response, aborting', r.status)
-                    self.write_loop_task = None
                     break
             else:
                 # websocket
@@ -690,3 +689,4 @@ async def _write_loop(self):
                         'aborting')
                     break
         self.logger.info('Exiting write loop task')
+        self.write_loop_task = None
diff --git a/src/engineio/client.py b/src/engineio/client.py
index e8865df..6fe4f4a 100644
--- a/src/engineio/client.py
+++ b/src/engineio/client.py
@@ -521,7 +521,7 @@ def _read_loop_polling(self):
 
     def _read_loop_websocket(self):
         """Read packets from the Engine.IO WebSocket connection."""
-        while self.state == 'connected':
+        while self.state == 'connected' and self.write_loop_task:
             p = None
             try:
                 p = self.ws.recv()
@@ -616,7 +616,6 @@ def _write_loop(self):
                 if r.status_code < 200 or r.status_code >= 300:
                     self.logger.warning('Unexpected status code %s in server '
                                         'response, aborting', r.status_code)
-                    self.write_loop_task = None
                     break
             else:
                 # websocket
@@ -634,3 +633,4 @@ def _write_loop(self):
                         'WebSocket connection was closed, aborting')
                     break
         self.logger.info('Exiting write loop task')
+        self.write_loop_task = None
diff --git a/tests/common/test_socket.py b/tests/common/test_socket.py
index f9b6176..20d13b2 100644
--- a/tests/common/test_socket.py
+++ b/tests/common/test_socket.py
@@ -101,7 +101,10 @@ def test_schedule_ping(self):
         s = socket.Socket(mock_server, 'sid')
         s.send = mock.MagicMock()
         s.schedule_ping()
-        time.sleep(0.05)
+        for _ in range(10):
+            time.sleep(0.05)
+            if s.last_ping is not None:
+                break
         assert s.last_ping is not None
         assert s.send.call_args_list[0][0][0].encode() == '2'