diff --git a/mmengine/hooks/logger_hook.py b/mmengine/hooks/logger_hook.py
index 04e5f07294..26cd35b7d3 100644
--- a/mmengine/hooks/logger_hook.py
+++ b/mmengine/hooks/logger_hook.py
@@ -304,4 +304,5 @@ def after_run(self, runner) -> None:
             if not self.keep_local:
                 os.remove(local_filepath)
                 runner.logger.info(f'{local_filepath} was removed due to the '
-                                   '`self.keep_local=False`')
+                                   '`self.keep_local=False`. You can check '
+                                   f'the running logs in {out_filepath}')
diff --git a/mmengine/runner/runner.py b/mmengine/runner/runner.py
index e2506dd8d1..345c9418dd 100644
--- a/mmengine/runner/runner.py
+++ b/mmengine/runner/runner.py
@@ -716,6 +716,11 @@ def build_logger(self,
 
         log_cfg = dict(log_level=log_level, log_file=log_file, **kwargs)
         log_cfg.setdefault('name', self._experiment_name)
+        # `torch.compile` in PyTorch 2.0 could close all user defined handlers
+        # unexpectedly. Using file mode 'a' can help prevent abnormal
+        # termination of the FileHandler and ensure that the log file could
+        # be continuously updated during the lifespan of the runner.
+        log_cfg.setdefault('file_mode', 'a')
 
         return MMLogger.get_instance(**log_cfg)  # type: ignore
 
diff --git a/tests/test_runner/test_runner.py b/tests/test_runner/test_runner.py
index a40c75317d..725b511ec7 100644
--- a/tests/test_runner/test_runner.py
+++ b/tests/test_runner/test_runner.py
@@ -1745,6 +1745,14 @@ def test_train_with_compile(self):
         runner = Runner.from_cfg(cfg)
         runner.train()
 
+        runner._maybe_compile('train_step')
+        # PyTorch 2.0.0 could close the FileHandler after calling of
+        # ``torch.compile``. So we need to test our file handler still works.
+        with open(osp.join(f'{runner.log_dir}',
+                           f'{runner.timestamp}.log')) as f:
+            last_line = f.readlines()[-1]
+            self.assertTrue(last_line.endswith('please be patient.\n'))
+
     def test_val(self):
         cfg = copy.deepcopy(self.epoch_based_cfg)
         cfg.experiment_name = 'test_val1'