I was wondering if anyone knew how many 10-time undefeated champions "Face the Music" had. The only one I know of is Sarabeth Rothfeld, did anyone else retire undefeated?

From what I recall seeing on FAM's reruns a decade ago, no.

Sarabeth Rothfeld was the only undefeated champion. In the second season, a champion stayed on until defeated. Toni Reel and Bill Ware both won 11 or 12 shows, and they won a Coachmen Camper Trailer for winning their 10th game. I don't recall if there was a special prize for winning the 15th game.