Also worth noting, combinations of advanced model controllers (like suped up Afterglows) have a tendency to stop talking to older model headsets, or even headsets that would be interchangeable with xbox 360
I frequently found myself unplugging and replugging the wired controller and/or headset controller port to reset being mute in party chat
One way of knowing if your headset is outdated is by checking the left sidebar to see if quick settings for controller audio and mic sensitivity are even displayed. If they aren't, chances are you'll lose connection to sound once in awhile when using a high end controller. Unplug and replug everything on the controller, switch to game chat and back, and it should be fine
Other than those areas, it's also possible time zones are making one player a shitty party host, so you can also experiment with which of you hosts the party