Other metabolic reactions aside, what causes beta oxidation to stop?
Different enzymes specialize to work on different size ranges. If the fatty acid is too short, it might not bind to enzymes that work on large fatty acids. An enzyme capable of binding short fatty acids might have most binding determinants targeting the CoA moiety instead of the fatty acid itself.


  At what point would this process stop ? lets say we have a short chain fatty acid like butanoate (4c) would it still transfer an acetyl group leaving an acetate molecule ?


It goes all the way as long as the CoA is attached.