diff --git a/src/socketio/async_client.py b/src/socketio/async_client.py
index 7bfd1ac3..0d85aa18 100644
--- a/src/socketio/async_client.py
+++ b/src/socketio/async_client.py
@@ -189,6 +189,9 @@ async def wait(self):
             await self.eio.wait()
             await self.sleep(1)  # give the reconnect task time to start up
             if not self._reconnect_task:
+                if self.eio.state == 'connected':  # pragma: no cover
+                    # connected while sleeping above
+                    continue
                 break
             await self._reconnect_task
             if self.eio.state != 'connected':
diff --git a/src/socketio/client.py b/src/socketio/client.py
index b5fa0b4e..00d7961e 100644
--- a/src/socketio/client.py
+++ b/src/socketio/client.py
@@ -180,7 +180,12 @@ def wait(self):
             self.eio.wait()
             self.sleep(1)  # give the reconnect task time to start up
             if not self._reconnect_task:
-                break
+                if self.eio.state == 'connected':  # pragma: no cover
+                    # connected while sleeping above
+                    continue
+                else:
+                    # the reconnect task gave up
+                    break
             self._reconnect_task.join()
             if self.eio.state != 'connected':
                 break