diff --git a/x-pack/plugin/ccr/src/main/java/org/elasticsearch/xpack/ccr/action/ShardFollowNodeTask.java b/x-pack/plugin/ccr/src/main/java/org/elasticsearch/xpack/ccr/action/ShardFollowNodeTask.java
index b156a41896a..7d1e96c5d7c 100644
--- a/x-pack/plugin/ccr/src/main/java/org/elasticsearch/xpack/ccr/action/ShardFollowNodeTask.java
+++ b/x-pack/plugin/ccr/src/main/java/org/elasticsearch/xpack/ccr/action/ShardFollowNodeTask.java
@@ -28,6 +28,8 @@ import org.elasticsearch.index.translog.Translog;
 import org.elasticsearch.indices.IndexClosedException;
 import org.elasticsearch.persistent.AllocatedPersistentTask;
 import org.elasticsearch.tasks.TaskId;
+import org.elasticsearch.transport.NodeDisconnectedException;
+import org.elasticsearch.transport.NodeNotConnectedException;
 import org.elasticsearch.xpack.ccr.action.bulk.BulkShardOperationsResponse;
 import org.elasticsearch.xpack.core.ccr.ShardFollowNodeTaskStatus;
 
@@ -371,6 +373,7 @@ public abstract class ShardFollowNodeTask extends AllocatedPersistentTask {
             scheduler.accept(TimeValue.timeValueMillis(delay), task);
         } else {
             fatalException = ExceptionsHelper.convertToElastic(e);
+            LOGGER.warn("shard follow task encounter non-retryable error", e);
         }
     }
 
@@ -399,7 +402,10 @@ public abstract class ShardFollowNodeTask extends AllocatedPersistentTask {
             actual instanceof AlreadyClosedException ||
             actual instanceof ElasticsearchSecurityException || // If user does not have sufficient privileges
             actual instanceof ClusterBlockException || // If leader index is closed or no elected master
-            actual instanceof IndexClosedException; // If follow index is closed
+            actual instanceof IndexClosedException || // If follow index is closed
+            actual instanceof NodeDisconnectedException ||
+            actual instanceof NodeNotConnectedException ||
+            (actual.getMessage() != null && actual.getMessage().contains("TransportService is closed"));
     }
 
     // These methods are protected for testing purposes:
diff --git a/x-pack/plugin/ccr/src/test/java/org/elasticsearch/xpack/ccr/IndexFollowingIT.java b/x-pack/plugin/ccr/src/test/java/org/elasticsearch/xpack/ccr/IndexFollowingIT.java
index d0cc41f22c2..926b439ea35 100644
--- a/x-pack/plugin/ccr/src/test/java/org/elasticsearch/xpack/ccr/IndexFollowingIT.java
+++ b/x-pack/plugin/ccr/src/test/java/org/elasticsearch/xpack/ccr/IndexFollowingIT.java
@@ -270,7 +270,6 @@ public class IndexFollowingIT extends CcrIntegTestCase {
         assertMaxSeqNoOfUpdatesIsTransferred(resolveLeaderIndex("index1"), resolveFollowerIndex("index2"), numberOfShards);
     }
 
-    @AwaitsFix(bugUrl = "https://github.com/elastic/elasticsearch/issues/34696")
     public void testFollowIndexAndCloseNode() throws Exception {
         getFollowerCluster().ensureAtLeastNumDataNodes(3);
         String leaderIndexSettings = getIndexSettings(3, 1, singletonMap(IndexSettings.INDEX_SOFT_DELETES_SETTING.getKey(), "true"));
@@ -587,7 +586,6 @@ public class IndexFollowingIT extends CcrIntegTestCase {
         assertThat(followerClient().prepareSearch("index2").get().getHits().getTotalHits(), equalTo(2L));
     }
 
-    @AwaitsFix(bugUrl = "https://github.com/elastic/elasticsearch/issues/34696")
     public void testFailOverOnFollower() throws Exception {
         int numberOfReplicas = between(1, 2);
         getFollowerCluster().startMasterOnlyNode();