Why they wouldn't sing the song...*SPOILERS*
When Streicher invited them over after the concert and asked them to sing "a German folk-song", Frommerman was unable to keep his composure. At first, I thought this was because the group was being demanded to sing an old German song for the Nazi officer, perhaps to drive home a point to the entertainers, but it wasn't until Bob's request that I realized it was more to do with the content of the song, and how it related to Harry, Bob, and Erna. At least, I think that was it.
It certainly must have seemed like a political move (not to sing) by Streicher, who was unaware of the forces pulling the members of the group.
Don't ask me to kill your dragon...