@Async not working after upgrading to Spring Boot 1.3.3

You need place your bean factory method in a other class annotated as @Configuration. Executor will be used for @Async method execution in this way.

@Configuration
@EnableAsync
public class AsyncConfig {
   @Bean(name = "myTaskExecutor")
   public ThreadPoolTaskExecutor myTaskExecutor() {
      return new ThreadPoolTaskExecutor();
   }
}

Injecting into configuration classes might be a challenge, I wouldn't recommend it especially if that class is also an actual bean. IMHO your class does too much. Next to that move the configuration of the ThreadPoolTaskExecutor where it belongs.

Instead of autowiring create a @Bean method which returns a CommandLineRunner instead of you implementing it.

@SpringBootApplication
@EnableAsync
public class App {

    private static final Logger log = LoggerFactory.getLogger(App.class);

    public static void main(String[] args) {
        SpringApplication.run(App.class, args);
    }

    @Bean
    public CommandLineRunner runner(AsyncClass async) {

      return new CommandLineRunner() {
        public void run(String... arg0) throws Exception {
            log.info("in run");
            async.start();
            log.info("done run");
        }      
      };

    }

    @Bean
    public ThreadPoolTaskExecutor taskExecutor() {

        ThreadPoolTaskExecutor bean = new ThreadPoolTaskExecutor();
        bean.setCorePoolSize(1);
        bean.setMaxPoolSize(1);
        bean.setQueueCapacity(10);
        bean.setThreadPriority(1);
        bean.setWaitForTasksToCompleteOnShutdown(true);
        return bean;
    }
}

And of course cleanup your AsyncClass.