diff --git a/br/pkg/storage/s3.go b/br/pkg/storage/s3.go
index 2ba28a39d0a09..14ff8fc717fb5 100644
--- a/br/pkg/storage/s3.go
+++ b/br/pkg/storage/s3.go
@@ -1108,17 +1108,17 @@ func (rl retryerWithLog) ShouldRetry(r *request.Request) bool {
 			r.Error = errors.New("read tcp *.*.*.*:*->*.*.*.*:*: read: connection reset by peer")
 		}
 	})
+	if r.HTTPRequest.URL.Host == ec2MetaAddress && (isDeadlineExceedError(r.Error) || isConnectionResetError(r.Error)) {
+		// fast fail for unreachable linklocal address in EC2 containers.
+		log.Warn("failed to get EC2 metadata. skipping.", logutil.ShortError(r.Error))
+		return false
+	}
 	if isConnectionResetError(r.Error) {
 		return true
 	}
 	if isConnectionRefusedError(r.Error) {
 		return false
 	}
-	if isDeadlineExceedError(r.Error) && r.HTTPRequest.URL.Host == ec2MetaAddress {
-		// fast fail for unreachable linklocal address in EC2 containers.
-		log.Warn("failed to get EC2 metadata. skipping.", logutil.ShortError(r.Error))
-		return false
-	}
 	return rl.DefaultRetryer.ShouldRetry(r)
 }
 
diff --git a/br/tests/br_full/run.sh b/br/tests/br_full/run.sh
index 78b28d51f8f4e..1753dfdc460d1 100755
--- a/br/tests/br_full/run.sh
+++ b/br/tests/br_full/run.sh
@@ -53,7 +53,7 @@ test_log="${TEST_DIR}/${DB}_test.log"
 error_str="not read from or written to within the timeout period"
 unset BR_LOG_TO_TERM
 
-export GO_FAILPOINTS="github.com/pingcap/tidb/br/pkg/backup/backup-storage-error=1*return(\"connection refused\")->1*return(\"InternalError\");github.com/pingcap/tidb/br/pkg/backup/backup-timeout-error=1*return(\"<Code>RequestTimeout</Code>\")->1*return(\"not read from or written to within the timeout period\")->1*return(\"<Code>InvalidPart</Code>\")""
+export GO_FAILPOINTS="github.com/pingcap/tidb/br/pkg/backup/backup-storage-error=1*return(\"connection refused\")->1*return(\"InternalError\");github.com/pingcap/tidb/br/pkg/backup/backup-timeout-error=1*return(\"<Code>RequestTimeout</Code>\")->1*return(\"not read from or written to within the timeout period\")->1*return(\"<Code>InvalidPart</Code>\")"
 run_br --pd $PD_ADDR backup full -s "local://$TEST_DIR/$DB-lz4" --concurrency 4 --compression lz4 --log-file $test_log
 export GO_FAILPOINTS=""
 size_lz4=$(du -d 0 $TEST_DIR/$DB-lz4 | awk '{print $1}')