I'm really not into the FAA world , but generally speaking , the no blame culture should be a must in the civil world wich the US should be part of....
During the investigation (the person in charge will download audio and radar tracking if needed) they can simply collect and close the matter at same time, if a serious event occurred they will continue but normally asking you about your side of the story and given that in the specific case you have no fault , nothing should be happening either to you, your licence and your professional life ....
According to your story, the reason can simply be addressed to technical issues, on the ATC side or even on your side, 'cause you're not guilty or responsable for a broken headset, airplane malfunction, o even a flying task wich caused your missing listening/reply, aviate than communicate .