diff --git a/ms_agent/cron/scheduler.py b/ms_agent/cron/scheduler.py
index a94acf304..8a2566c4f 100644
--- a/ms_agent/cron/scheduler.py
+++ b/ms_agent/cron/scheduler.py
@@ -83,10 +83,11 @@ def _arm_timer(self) -> None:
         self._timer_task = asyncio.ensure_future(self._sleep_and_tick(delay_s))
 
     def _get_earliest_due_ms(self) -> Optional[int]:
-        """Find the earliest next_run_at among enabled, non-paused jobs."""
+        """Find the earliest next_run_at among dispatchable jobs."""
         earliest = None
         for job, state in self._repo.load_all_with_state():
-            if not job.enabled or state.status == 'paused':
+            if not job.enabled or state.status in ('paused', 'running',
+                                                   'completed'):
                 continue
             ms = _iso_to_ms(state.next_run_at)
             if ms is not None and (earliest is None or ms < earliest):
diff --git a/tests/cron/test_scheduler.py b/tests/cron/test_scheduler.py
index 0454f180d..dce2af10d 100644
--- a/tests/cron/test_scheduler.py
+++ b/tests/cron/test_scheduler.py
@@ -39,6 +39,42 @@ def test_invalid_returns_none(self):
 
 
 class TestAsyncScheduler:
+    @pytest.mark.asyncio
+    @pytest.mark.parametrize('status', ['running', 'completed'])
+    @pytest.mark.parametrize('has_scheduled_job', [False, True])
+    async def test_timer_ignores_non_dispatchable_jobs(
+            self, repo, monkeypatch, status, has_scheduled_job):
+        now = 1800000000000
+        monkeypatch.setattr('ms_agent.cron.scheduler._now_ms', lambda: now)
+        past = datetime.fromtimestamp(
+            (now - 10000) / 1000, timezone.utc).isoformat()
+        repo.save_job_and_state(
+            CronJobSpec(id='inactive', prompt='test'),
+            CronJobState(status=status, next_run_at=past))
+        if has_scheduled_job:
+            future = datetime.fromtimestamp(
+                (now + 30000) / 1000, timezone.utc).isoformat()
+            repo.save_job_and_state(
+                CronJobSpec(id='scheduled', prompt='test'),
+                CronJobState(status='scheduled', next_run_at=future))
+
+        delays = []
+
+        async def on_due(jobs):
+            pytest.fail('No jobs should be dispatched')
+
+        async def capture_delay(delay):
+            delays.append(delay)
+
+        scheduler = AsyncScheduler(repo, on_due=on_due, tick_interval=60)
+        monkeypatch.setattr(scheduler, '_sleep_and_tick', capture_delay)
+        await scheduler.start()
+        try:
+            await asyncio.sleep(0)
+            assert delays == [30 if has_scheduled_job else 60]
+        finally:
+            scheduler.stop()
+
     @pytest.mark.asyncio
     async def test_start_stop(self, repo):
         due_list = []