Good communication is key and if I can't communicate with the agent I might just call the broker or office to find out if there might be a reason. At least good realtor always keep in touch and have the decency to keep you up to speed, even if their clients haven't replied yet.
Unfortunately, yes if after several attempts no response them I'd contact the broker. I hate to do that to my colleagues but there has to be a sense of professionalism.
Often times, it is not the agent that is silent but his client. With that said though, the agent should be contacting you to tell you that they are still waiting for response from their client. If after leaving a message on phone, text, and email that you have not heard from an agent warned that you will be contacting their broker if no response within 24 hours, then after 24 hours, by all means contact their broker. Who knows? maybe the agent has fallen over dead or had an accident. I firmly believe that on important messages that they should be verbal phone message, text mail, and email. Don't depend on one method. It is a rooky mistake.