This is my first post, but I have encountered an issue similar to this before. I work for a company that makes Bluetooth headsets, primarily for truckers, and this is a fairly often related experience. I would describe it as "dead air" on a phone call. Often, if the headset supports it, the A2DP stream will be fine. I don't know why, or where we found this from, but we have found that often if a user goes into their application settings, to "All" apps, there will be an app there titled "Bluetooth Share". Sometimes there is more than one, but only one with show an amount of data. Going into this, clearing that data, then restarting the phone has been reported to help resolve this issue.
Try it, and see what happens. Not just Motorola phones do this either, but it seems to be associated with Android 4.0.x and up.