diff --git a/br/pkg/streamhelper/basic_lib_for_test.go b/br/pkg/streamhelper/basic_lib_for_test.go
index 5e847a6ea78c4..1dff77dd72864 100644
--- a/br/pkg/streamhelper/basic_lib_for_test.go
+++ b/br/pkg/streamhelper/basic_lib_for_test.go
@@ -134,7 +134,7 @@ func (t trivialFlushStream) Recv() (*logbackup.SubscribeFlushEventResponse, erro
 			return &item, nil
 		default:
 		}
-		return nil, t.cx.Err()
+		return nil, status.Error(codes.Canceled, t.cx.Err().Error())
 	}
 }
 
diff --git a/br/pkg/streamhelper/flush_subscriber.go b/br/pkg/streamhelper/flush_subscriber.go
index 64607e68858f8..70cd4d8e4501d 100644
--- a/br/pkg/streamhelper/flush_subscriber.go
+++ b/br/pkg/streamhelper/flush_subscriber.go
@@ -211,12 +211,14 @@ func (s *subscription) connect(ctx context.Context, dialer LogBackupService) {
 
 func (s *subscription) doConnect(ctx context.Context, dialer LogBackupService) error {
 	log.Info("[log backup subscription manager] Adding subscription.", zap.Uint64("store", s.storeID), zap.Uint64("boot", s.storeBootAt))
-	s.clearError()
+	// We should shutdown the background task firstly.
+	// Once it yields some error during shuting down, the error won't be brought to next run.
 	s.close()
+	s.clearError()
 
 	c, err := dialer.GetLogBackupClient(ctx, s.storeID)
 	if err != nil {
-		return err
+		return errors.Annotate(err, "failed to get log backup client")
 	}
 	cx, cancel := context.WithCancel(ctx)
 	cli, err := c.SubscribeFlushEvent(cx, &logbackup.SubscribeFlushEventRequest{
@@ -224,7 +226,7 @@ func (s *subscription) doConnect(ctx context.Context, dialer LogBackupService) e
 	})
 	if err != nil {
 		cancel()
-		return err
+		return errors.Annotate(err, "failed to subscribe events")
 	}
 	s.cancel = cancel
 	s.background = spawnJoinable(func() { s.listenOver(cli) })
@@ -249,7 +251,7 @@ func (s *subscription) listenOver(cli eventStream) {
 		msg, err := cli.Recv()
 		if err != nil {
 			log.Info("[log backup flush subscriber] Listen stopped.", zap.Uint64("store", storeID), logutil.ShortError(err))
-			if err == io.EOF || err == context.Canceled {
+			if err == io.EOF || err == context.Canceled || status.Code(err) == codes.Canceled {
 				return
 			}
 			s.emitError(errors.Annotatef(err, "while receiving from store id %d", storeID))
diff --git a/br/pkg/streamhelper/subscription_test.go b/br/pkg/streamhelper/subscription_test.go
index 519801ce2b448..2341cb05dc01e 100644
--- a/br/pkg/streamhelper/subscription_test.go
+++ b/br/pkg/streamhelper/subscription_test.go
@@ -11,6 +11,8 @@ import (
 	"github.com/pingcap/tidb/br/pkg/streamhelper"
 	"github.com/pingcap/tidb/br/pkg/streamhelper/spans"
 	"github.com/stretchr/testify/require"
+	"google.golang.org/grpc/codes"
+	"google.golang.org/grpc/status"
 )
 
 func installSubscribeSupport(c *fakeCluster) {
@@ -105,6 +107,25 @@ func TestHasFailureStores(t *testing.T) {
 	req.NoError(sub.PendingErrors())
 }
 
+func TestStoreOffline(t *testing.T) {
+	req := require.New(t)
+	ctx := context.Background()
+	c := createFakeCluster(t, 4, true)
+	c.splitAndScatter("0001", "0002", "0003", "0008", "0009")
+	installSubscribeSupport(c)
+
+	c.onGetClient = func(u uint64) error {
+		return status.Error(codes.DataLoss, "upon an eclipsed night, some of data (not all data) have fled from the dataset")
+	}
+	sub := streamhelper.NewSubscriber(c, c)
+	req.NoError(sub.UpdateStoreTopology(ctx))
+	req.Error(sub.PendingErrors())
+
+	c.onGetClient = nil
+	sub.HandleErrors(ctx)
+	req.NoError(sub.PendingErrors())
+}
+
 func TestStoreRemoved(t *testing.T) {
 	req := require.New(t)
 	ctx := context.Background()