diff --git a/zerver/worker/queue_processors.py b/zerver/worker/queue_processors.py
index 20e0e3db59..7f4cc5e9e8 100644
--- a/zerver/worker/queue_processors.py
+++ b/zerver/worker/queue_processors.py
@@ -657,56 +657,69 @@ class MissedMessageWorker(QueueProcessingWorker):
 
     def work(self) -> None:
         while True:
-            with self.cv:
+            try:
+                finished = self.background_loop()
+                if finished:
+                    break
+            except Exception:
+                logging.exception(
+                    "Exception in MissedMessage background worker; restarting the loop",
+                    stack_info=True,
+                )
+
+    def background_loop(self) -> bool:
+        with self.cv:
+            if self.stopping:
+                return True
+            # There are three conditions which we wait for:
+            #
+            #  1. We are being explicitly asked to stop; see the
+            #     notify() call in stop()
+            #
+            #  2. We have no ScheduledMessageNotificationEmail
+            #     objects currently (has_timeout = False) and the
+            #     first one was just enqueued; see the notify()
+            #     call in consume().  We break out so that we can
+            #     come back around the loop and re-wait with a
+            #     timeout (see next condition).
+            #
+            #  3. One or more ScheduledMessageNotificationEmail
+            #     exist in the database, so we need to re-check
+            #     them regularly; this happens by hitting the
+            #     timeout and calling maybe_send_batched_emails().
+            #     There is no explicit notify() for this.
+            timeout: Optional[int] = None
+            if ScheduledMessageNotificationEmail.objects.exists():
+                timeout = self.CHECK_FREQUENCY_SECONDS
+            self.has_timeout = timeout is not None
+
+            def wait_condition() -> bool:
                 if self.stopping:
-                    return
-                # There are three conditions which we wait for:
-                #
-                #  1. We are being explicitly asked to stop; see the
-                #     notify() call in stop()
-                #
-                #  2. We have no ScheduledMessageNotificationEmail
-                #     objects currently (has_timeout = False) and the
-                #     first one was just enqueued; see the notify()
-                #     call in consume().  We break out so that we can
-                #     come back around the loop and re-wait with a
-                #     timeout (see next condition).
-                #
-                #  3. One or more ScheduledMessageNotificationEmail
-                #     exist in the database, so we need to re-check
-                #     them regularly; this happens by hitting the
-                #     timeout and calling maybe_send_batched_emails().
-                #     There is no explicit notify() for this.
-                timeout: Optional[int] = None
-                if ScheduledMessageNotificationEmail.objects.exists():
-                    timeout = self.CHECK_FREQUENCY_SECONDS
-                self.has_timeout = timeout is not None
+                    # Condition (1)
+                    return True
+                if timeout is None:
+                    # Condition (2).  We went to sleep with no
+                    # ScheduledMessageNotificationEmail existing,
+                    # and one has just been made.  We re-check
+                    # that is still true now that we have the
+                    # lock, and if we see it, we stop waiting.
+                    return ScheduledMessageNotificationEmail.objects.exists()
+                # This should only happen at the start or end of
+                # the wait, when we haven't been notified, but are
+                # re-checking the condition.
+                return False
 
-                def wait_condition() -> bool:
-                    if self.stopping:
-                        # Condition (1)
-                        return True
-                    if timeout is None:
-                        # Condition (2).  We went to sleep with no
-                        # ScheduledMessageNotificationEmail existing,
-                        # and one has just been made.  We re-check
-                        # that is still true now that we have the
-                        # lock, and if we see it, we stop waiting.
-                        return ScheduledMessageNotificationEmail.objects.exists()
-                    # This should only happen at the start or end of
-                    # the wait, when we haven't been notified, but are
-                    # re-checking the condition.
-                    return False
+            was_notified = self.cv.wait_for(wait_condition, timeout=timeout)
 
-                was_notified = self.cv.wait_for(wait_condition, timeout=timeout)
+        # Being notified means that we are in conditions (1) or
+        # (2), above.  In neither case do we need to look at if
+        # there are batches to send -- (2) means that the
+        # ScheduledMessageNotificationEmail was _just_ created, so
+        # there is no need to check it now.
+        if not was_notified:
+            self.maybe_send_batched_emails()
 
-            # Being notified means that we are in conditions (1) or
-            # (2), above.  In neither case do we need to look at if
-            # there are batches to send -- (2) means that the
-            # ScheduledMessageNotificationEmail was _just_ created, so
-            # there is no need to check it now.
-            if not was_notified:
-                self.maybe_send_batched_emails()
+        return False
 
     def maybe_send_batched_emails(self) -> None:
         current_time = timezone_now()