Fiddler's Companion misuse the html a bit in their abc: To change to a new line, they start a new paragraph, rather than use a line break. A paragraph will normally leave a white line between the lines, but they catch that by using a style that shrinks that white line to almost nothing.
Unfortunately, that means that if you try to copy their abc code, you will get the extra white lines as well. Apparently, concertina.net was not built to accept weird things like that, and conversion fails.
I wonder if this is solvable. I'll contact CONCERTINA.net to see what they say.