diff --git a/src/sentry/consumers/dlq.py b/src/sentry/consumers/dlq.py
index 4e8ea5f7939d25..eb3e7e1fec89b8 100644
--- a/src/sentry/consumers/dlq.py
+++ b/src/sentry/consumers/dlq.py
@@ -7,7 +7,11 @@
 
 from arroyo.backends.kafka import KafkaPayload, KafkaProducer
 from arroyo.dlq import InvalidMessage, KafkaDlqProducer
-from arroyo.processing.strategies.abstract import ProcessingStrategy, ProcessingStrategyFactory
+from arroyo.processing.strategies.abstract import (
+    MessageRejected,
+    ProcessingStrategy,
+    ProcessingStrategyFactory,
+)
 from arroyo.types import FILTERED_PAYLOAD, BrokerValue, Commit, FilteredPayload, Message, Partition
 from arroyo.types import Topic as ArroyoTopic
 from arroyo.types import Value
@@ -127,9 +131,12 @@ def poll(self) -> None:
         if self.offsets_to_forward:
             if time.time() > self.last_forwarded_offsets + 1:
                 filtered_message = Message(Value(FILTERED_PAYLOAD, self.offsets_to_forward))
-                self.next_step.submit(filtered_message)
-                self.offsets_to_forward = {}
-                self.last_forwarded_offsets = time.time()
+                try:
+                    self.next_step.submit(filtered_message)
+                    self.offsets_to_forward = {}
+                    self.last_forwarded_offsets = time.time()
+                except MessageRejected:
+                    pass
 
     def join(self, timeout: float | None = None) -> None:
         self.next_step.join(timeout)