diff --git a/swh/journal/client.py b/swh/journal/client.py
--- a/swh/journal/client.py
+++ b/swh/journal/client.py
@@ -5,6 +5,7 @@
 
 from collections import defaultdict
 from importlib import import_module
+from itertools import cycle
 import logging
 import os
 from typing import Any, Callable, Dict, List, Optional, Set, Tuple, Union
@@ -293,22 +294,31 @@
                     batch_size = min(
                         self.stop_after_objects - total_objects_processed, batch_size,
                     )
-
                 set_status("waiting")
-                while True:
+                for i in cycle(reversed(range(10))):
                     messages = self.consumer.consume(
                         timeout=timeout, num_messages=batch_size
                     )
                     if messages:
                         break
+                    if self.stop_on_eof and i == 0:
+                        at_eof = all(
+                            (tp.topic, tp.partition) in self.eof_reached
+                            for tp in self.consumer.assignment()
+                        )
+                        if at_eof:
+                            break
+                if messages:
+                    set_status("processing")
+                    batch_processed, at_eof = self.handle_messages(messages, worker_fn)
+
+                    set_status("idle")
+                    # report the number of handled messages
+                    statsd.increment(
+                        JOURNAL_MESSAGE_NUMBER_METRIC, value=batch_processed
+                    )
+                    total_objects_processed += batch_processed
 
-                set_status("processing")
-                batch_processed, at_eof = self.handle_messages(messages, worker_fn)
-
-                set_status("idle")
-                # report the number of handled messages
-                statsd.increment(JOURNAL_MESSAGE_NUMBER_METRIC, value=batch_processed)
-                total_objects_processed += batch_processed
                 if at_eof:
                     break