diff --git a/python/ray/tune/trainable.py b/python/ray/tune/trainable.py
index f550b3122..cf6d7c0b3 100644
--- a/python/ray/tune/trainable.py
+++ b/python/ray/tune/trainable.py
@@ -625,10 +625,12 @@ class Trainable:
             self._stdout_stream.flush()
             self._stdout_context.__exit__(None, None, None)
             self._stdout_fp.close()
+            self._stdout_context = None
         if self._stderr_context:
             self._stderr_stream.flush()
             self._stderr_context.__exit__(None, None, None)
             self._stderr_fp.close()
+            self._stderr_context = None
 
     def stop(self):
         """Releases all resources used by this trainable.