diff --git a/swh/journal/client.py b/swh/journal/client.py
--- a/swh/journal/client.py
+++ b/swh/journal/client.py
@@ -6,7 +6,6 @@
 from collections import defaultdict
 import logging
 import os
-import time
 from typing import Any, Callable, Dict, List, Optional, Set, Tuple, Union
 
 from confluent_kafka import Consumer, KafkaError, KafkaException
@@ -220,10 +219,16 @@
         self.subscribe()
 
         self.stop_after_objects = stop_after_objects
-        self.process_timeout = process_timeout
+
         self.eof_reached: Set[Tuple[str, str]] = set()
         self.batch_size = batch_size
 
+        if process_timeout is not None:
+            raise DeprecationWarning(
+                "'process_timeout' argument is not supported anymore by "
+                "JournalClient; please remove it from your configuration.",
+            )
+
     def subscribe(self):
         """Subscribe to topics listed in self.subscription
 
@@ -241,26 +246,11 @@
                                                        the messages as
                                                        argument.
         """
-        start_time = time.monotonic()
         total_objects_processed = 0
+        # timeout for message poll
+        timeout = 1.0
 
         while True:
-            # timeout for message poll
-            timeout = 1.0
-
-            elapsed = time.monotonic() - start_time
-            if self.process_timeout:
-                # +0.01 to prevent busy-waiting on / spamming consumer.poll.
-                # consumer.consume() returns shortly before X expired
-                # (a matter of milliseconds), so after it returns a first
-                # time, it would then be called with a timeout in the order
-                # of milliseconds, therefore returning immediately, then be
-                # called again, etc.
-                if elapsed + 0.01 >= self.process_timeout:
-                    break
-
-                timeout = self.process_timeout - elapsed
-
             batch_size = self.batch_size
             if self.stop_after_objects:
                 if total_objects_processed >= self.stop_after_objects: