Fuel that doesn't get burned in the engine but then passes through to the catalytic converter can cause a catalytic converter to fail prematurely.
Fuel that is not burned properly during the combustion cycle of the engine can be caused by a bad oxygen sensor, bad or dirty mass air flow sensor or other things that cause an engine misfire such as bad ignition coils, bad spark plugs etc.
keeping your engine running in tip top shape will save your catalytic converter from needing replaced so soon as well as improve your fuel mileage.