I'll add my experience here.
Throughout the Hinterlands I adventured with Cassandra, Varric, and Solas. I remember getting some banter and music, then after a while it stopped completely. I assumed that the group had said all they were going to say, so I went to a new zone (Storm Coast). Hours went by with no banter, and that is when I hit up the forums and found out about the bug. So I went there with Blackwall, Sera and Vivienne who I had recruited in the meantime but had never adventured with. Nothing. I checked into Val Royeaux. No music either. Damn, I had the banter bug.
So I went into my completed quests and scrolled through them, and was spammed by the Quest Complete message upon exiting the journal. For good measure I did the same for all Codex entries. Fast travelled from the War Room to Storm Coast, and then Val Royeaux where I was greeted by music!
Confident that the bug was resolved, I went back to the Storm Coast where Blackwall asked Sera how the end of a story she had told went. What story? I thought, they had been mute up until now. I guess I'll have to Youtube the banter. So it seems to me that the program *thinks* it's playing the party banter, but in actuality nothing is happening.
Since then I have been careful to fast travel from the War Room (and never back out of it) and also keep my Completed Quest/Journal clear. I have had no banter issues again as a result of this for which I am very happy.
I just wanted to highlight my experience because I cannot understate how much better the game is with the party banter. I have been extremely tempted to start again (due to the bug, plus I'd like to tweak my character's appearance) but I was already 40 hours in, so I haven't.
I really hope you can find a fix for this Bioware because it is a major feature, plus most of it is so good! It's a shame it's being missed.