If my public defender is not communicating with me, can I request another?

The short answer is that you can ask, but expect for the judge to deny your request. Under the Sixth Amendment, you have the right to an appointed attorney--but not the right to choose which appointed attorney you get!

Public defenders are like anything else: Some are great, some are lousy, and many are good. But all public defenders are overloaded with cases. I remember preparing cases for trial during the day, interviewing witnesses and drafting motions, and then listening to my voicemails at 6pm to make a list of people to call back. Sometimes it would take me an hour just to listen to all of them!

If you're not getting a call back--or a response to a letter or email--it's difficult to know if your attorney is busy or a bad attorney. See if you can schedule a face-to-face meeting with your public defender. If you can't get a hold of him to do that, call the main office line and see if an administrative assistant or supervisor can schedule a meeting for you. If leaving voicemails isn't working, write emails and letters. 

But you also need realistic expectations. A public defender's time is extremely limited, and he or she is focusing on what's happening in court next week--not next month. You deserve to have an attorney who is zealously representing you in court, so don't give up trying to communicate with your public defender.