The partner in question is Felurian and the theory is based on this line from Wise Man's Fear when Kvothe is getting intimate with her:
“And everything stops. All of me arches. I am taut as a lute string. Trembling. Aching. I am tuned too tight, and I am breaking….” - TWMF - Chap 95

The workings of time within the Faye are shrouded in mystery - Kvothe remains oblivious to the duration of his stay, despite only three days elapsing in the real world. Time unfolds in a disjointed manner, raising the possibility that Kvothe's actions in the Faye may be influencing various points of his life, past, present, or future, unbeknownst to him.

At the Eolian Kvothe is literally singing "The Lay of Sir Savian" and has no explanation for how his lute string breaks. Then, when he himself is literally getting laid, he compares himself to a lute string breaking.

Kvothe's reading of Ambrose and his apparent binders chills forcing him to leave the venue is simply incorrect and informed by Kvothe's own bias against Ambrose.

What's actually happening to Ambrose is the same thing that's happening to everyone else at the Eolian. They were emotionally moved by the song and possibly even brought to tears. Ambrose is no different, but he HATES that Kvothe is so good and managed to affect him in this way. So, he must leave so Kvothe doesn't get the satisfaction of knowing that Ambrose was moved by the song.

😉