diff --git a/airflow/jobs/scheduler_job_runner.py b/airflow/jobs/scheduler_job_runner.py
index e05ad770a470..4eebf9967cd2 100644
--- a/airflow/jobs/scheduler_job_runner.py
+++ b/airflow/jobs/scheduler_job_runner.py
@@ -815,7 +815,7 @@ def _execute(self) -> int | None:
 
         processor_timeout_seconds: int = conf.getint("core", "dag_file_processor_timeout")
         processor_timeout = timedelta(seconds=processor_timeout_seconds)
-        if not self._standalone_dag_processor:
+        if not self._standalone_dag_processor and not self.processor_agent:
             self.processor_agent = DagFileProcessorAgent(
                 dag_directory=Path(self.subdir),
                 max_runs=self.num_times_parse_dags,
diff --git a/tests/jobs/test_scheduler_job.py b/tests/jobs/test_scheduler_job.py
index 195b9fce5e52..5e83c77a6463 100644
--- a/tests/jobs/test_scheduler_job.py
+++ b/tests/jobs/test_scheduler_job.py
@@ -3034,11 +3034,6 @@ def run_with_error(ti, ignore_ti_state=False):
         ti.refresh_from_db()
         assert ti.state == State.SUCCESS
 
-    # TODO: Investigate super-mysterious behaviour of this test hanging for sqlite. This test started
-    # To fail ONLY on sqlite but only on self-hosted runners and locally (not on public runners)
-    # We should uncomment it when we figure out what's going on
-    # Issue: https://github.com/apache/airflow/issues/35204
-    @pytest.mark.backend("mssql", "mysql", "postgres")
     def test_retry_handling_job(self):
         """
         Integration test of the scheduler not accidentally resetting