diff --git a/src/monitor_utils/runner.py b/src/monitor_utils/runner.py
index 645601d..bbc34d9 100644
--- a/src/monitor_utils/runner.py
+++ b/src/monitor_utils/runner.py
@@ -556,7 +556,12 @@ async def retry_failed_pages(
 
 
 def first_error(group_exc: BaseExceptionGroup) -> BaseException:
-    """Return the first leaf exception of a possibly nested exception group."""
+    """Return a leaf exception of a possibly nested group, preferring an
+    unexpected one so a real bug is never masked by a routine network error."""
+    _, unexpected = group_exc.split(EXPECTED_TASK_ERRORS)
+    if unexpected is not None:
+        group_exc = unexpected
+
     error = group_exc.exceptions[0]
     while isinstance(error, BaseExceptionGroup):
         error = error.exceptions[0]