From the Wikipedia article on Virgil Thomson:
"[...] Thomson was famous for his revival of the rare technique of composing "musical portraits" of living subjects, often spending hours in a room with them before rushing off to finish the piece on his own. Many subjects reported feeling that the pieces did capture something unique about their identities even thought nearly all the portraits were absent of any clearly representational content."
A sly strip. Schroeder's looks of concentration, followed by his throwing his hands up, are important for understanding that he's giving up. I think it works better this way, allowing us to see him throwing in the towel, than being told directly that he's got nothing, which would seem a bit harder on Charlie Brown's feelings.