diff --git a/balancer_test.go b/balancer_test.go
index b01b998e..a101fe15 100644
--- a/balancer_test.go
+++ b/balancer_test.go
@@ -320,3 +320,57 @@ func TestGetOnWaitChannel(t *testing.T) {
 	cc.Close()
 	servers[0].stop()
 }
+
+func TestOneConnectionDown(t *testing.T) {
+	// Start 2 servers.
+	numServers := 2
+	servers, r := startServers(t, numServers, math.MaxUint32)
+	cc, err := Dial("foo.bar.com", WithBalancer(RoundRobin(r)), WithBlock(), WithInsecure(), WithCodec(testCodec{}))
+	if err != nil {
+		t.Fatalf("Failed to create ClientConn: %v", err)
+	}
+	// Add servers[1] to the service discovery.
+	var updates []*naming.Update
+	updates = append(updates, &naming.Update{
+		Op:   naming.Add,
+		Addr: "127.0.0.1:" + servers[1].port,
+	})
+	r.w.inject(updates)
+	req := "port"
+	var reply string
+	// Loop until servers[1] is up
+	for {
+		if err := Invoke(context.Background(), "/foo/bar", &req, &reply, cc); err != nil && ErrorDesc(err) == servers[1].port {
+			break
+		}
+		time.Sleep(10 * time.Millisecond)
+	}
+
+	var wg sync.WaitGroup
+	numRPC := 100
+	sleepDuration := 10 * time.Millisecond
+	wg.Add(1)
+	go func() {
+		time.Sleep(sleepDuration)
+		// After sleepDuration, kill server[0].
+		servers[0].stop()
+		wg.Done()
+	}()
+
+	// All non-failfast RPCs should not block because there's at least one connection available.
+	for i := 0; i < numRPC; i++ {
+		wg.Add(1)
+		go func() {
+			time.Sleep(sleepDuration)
+			// After sleepDuration, invoke RPC.
+			// server[0] is killed around the same time to make it racey between balancer and gRPC internals.
+			Invoke(context.Background(), "/foo/bar", &req, &reply, cc, FailFast(false))
+			wg.Done()
+		}()
+	}
+	wg.Wait()
+	cc.Close()
+	for i := 0; i < numServers; i++ {
+		servers[i].stop()
+	}
+}