Whether a line breaks depends upon the formatting assigned to that text in the document as well as the CopyFit parameters that you have selected to fit that text.

For those using the latest version of AccurioPro and CopyFit, you can select the CopyFit Method named No Break: Fit. This method will prevent lines from wrapping (breaking) while shrinking text to fit. 

If you prefer to apply a different CopyFit method, or if you are using an older version of AccurioPro and CopyFit, you can prevent text from breaking to a new line by assigning the InDesign No Break character format (the No Break setting is available in the InDesign Character panel menu).