on the skids vs weakening

on the skids

prep
  • In decline; going downhill; in trouble. 

weakening

noun
  • A structural principle of mathematical logic that states that the hypotheses of any derived fact may be freely extended with additional assumptions. 

  • An instance or process of loss of strength. 

How often have the words on the skids and weakening occurred in a corpus of books? (source: Google Ngram Viewer )