How to Detect cause of 503 Service Temporarily Unavailable error and handle it?

There is of course some apache log files. Search in your apache configuration files for 'Log' keyword, you'll certainly find plenty of them. Depending on your OS and installation places may vary (in a Typical Linux server it would be /var/log/apache2/[access|error].log).

Having a 503 error in Apache usually means the proxied page/service is not available. I assume you're using tomcat and that means tomcat is either not responding to apache (timeout?) or not even available (down? crashed?). So chances are that it's a configuration error in the way to connect apache and tomcat or an application inside tomcat that is not even sending a response for apache.

Sometimes, in production servers, it can as well be that you get too much traffic for the tomcat server, apache handle more request than the proxyied service (tomcat) can accept so the backend became unavailable.