The Collaborative International Dictionary of English v.0.48:

Frazzle \Fraz"zle\, n.
   1. The act or result of frazzling; the condition or quality
      of being frazzled; the tag end; a frayed-out end. [Prov.
      Eng. & U. S.]
      [Webster 1913 Suppl. +PJC]

            My fingers are all scratched to frazzles. --Kipling.
      [Webster 1913 Suppl.]

   2. a state of extreme exhaustion; -- often used in the phrase

   worn to a frazzle. [WordNet sense 1]
      [WordNet 1.5]

            Gordon had sent word to Lee that he "had fought his
            corps to a frazzle."                  --Nicolay &
                                                  Hay (Life of
                                                  Lincoln).
      [Webster 1913 Suppl.]