OK. I've narrowed down the problem. The headset stops working when I press the middle button to receive calls. In other words, if I answer a call using the actual phone, the headset works fine. If I do press the middle button to receive a call, I can no longer hear the other person nor can they hear me through the headset.
Does anyone use the iphone 5 headset with the galaxy s3? Does the headset work for you?