diff --git a/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/datafeed/DatafeedJob.java b/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/datafeed/DatafeedJob.java
index 22ebff57a4ba8..55064dd3e38d7 100644
--- a/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/datafeed/DatafeedJob.java
+++ b/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/datafeed/DatafeedJob.java
@@ -117,7 +117,13 @@ public Integer getMaxEmptySearches() {
     }
 
     public void finishReportingTimingStats() {
-        timingStatsReporter.finishReporting();
+        try {
+            timingStatsReporter.finishReporting();
+        } catch (Exception e) {
+            // We don't want the exception to propagate out of this method as it can leave the datafeed in the "stopping" state forever.
+            // Since persisting datafeed timing stats is not critical, we just log a warning here.
+            LOGGER.warn("[{}] Datafeed timing stats could not be reported due to: {}", jobId, e);
+        }
     }
 
     Long runLookBack(long startTime, Long endTime) throws Exception {
diff --git a/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/datafeed/DatafeedManager.java b/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/datafeed/DatafeedManager.java
index 2b7a40abc2e36..7a057f67eb390 100644
--- a/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/datafeed/DatafeedManager.java
+++ b/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/datafeed/DatafeedManager.java
@@ -361,7 +361,7 @@ public void stop(String source, TimeValue timeout, Exception e, boolean autoClos
                     acquired = datafeedJobLock.tryLock(timeout.millis(), TimeUnit.MILLISECONDS);
                 } catch (InterruptedException e1) {
                     Thread.currentThread().interrupt();
-                } finally {
+                } finally {  // It is crucial that none of the calls this "finally" block makes throws an exception for minor problems.
                     logger.info("[{}] stopping datafeed [{}] for job [{}], acquired [{}]...", source, datafeedId,
                             datafeedJob.getJobId(), acquired);
                     runningDatafeedsOnThisNode.remove(allocationId);
diff --git a/x-pack/plugin/ml/src/test/java/org/elasticsearch/xpack/ml/datafeed/DatafeedJobTests.java b/x-pack/plugin/ml/src/test/java/org/elasticsearch/xpack/ml/datafeed/DatafeedJobTests.java
index b28480354d9b6..1abb1291b17a7 100644
--- a/x-pack/plugin/ml/src/test/java/org/elasticsearch/xpack/ml/datafeed/DatafeedJobTests.java
+++ b/x-pack/plugin/ml/src/test/java/org/elasticsearch/xpack/ml/datafeed/DatafeedJobTests.java
@@ -12,6 +12,7 @@
 import org.elasticsearch.client.Client;
 import org.elasticsearch.common.bytes.BytesArray;
 import org.elasticsearch.common.settings.Settings;
+import org.elasticsearch.common.util.concurrent.EsRejectedExecutionException;
 import org.elasticsearch.common.util.concurrent.ThreadContext;
 import org.elasticsearch.common.xcontent.ToXContent;
 import org.elasticsearch.common.xcontent.XContentBuilder;
@@ -60,6 +61,7 @@
 import static org.mockito.Matchers.eq;
 import static org.mockito.Matchers.same;
 import static org.mockito.Mockito.atMost;
+import static org.mockito.Mockito.doThrow;
 import static org.mockito.Mockito.mock;
 import static org.mockito.Mockito.never;
 import static org.mockito.Mockito.times;
@@ -454,6 +456,15 @@ public void testFlushAnalysisProblemIsConflict() {
         assertThat(analysisProblemException.shouldStop, is(true));
     }
 
+    public void testFinishReportingTimingStats() {
+        doThrow(new EsRejectedExecutionException()).when(timingStatsReporter).finishReporting();
+
+        long frequencyMs = 100;
+        long queryDelayMs = 1000;
+        DatafeedJob datafeedJob = createDatafeedJob(frequencyMs, queryDelayMs, 1000, -1, randomBoolean());
+        datafeedJob.finishReportingTimingStats();
+    }
+
     private DatafeedJob createDatafeedJob(long frequencyMs, long queryDelayMs, long latestFinalBucketEndTimeMs,
                                           long latestRecordTimeMs, boolean haveSeenDataPreviously) {
         Supplier<Long> currentTimeSupplier = () -> currentTime;