To answer your question... a too-rich engine can cause raw fuel to reach the catalytic converter nd it can literally burn out. If your engine is consuming oil, it may be the 'fuel' that is burning up your catalytic converter.
The Nissan engines have won awards the world over... you apparently have one of the very few that has a problem. If you do not address the oil-consumption, it may continue to burn-up catalytic converters.
Are you aware that the catalytic converter is covered by your FEDERAL EMMISSIONS WARANTEE? This warantee often goes for 10years/100K miles. (Varies based on your vehicle.) The intent is that the Federal government is forcing the *manufacturers* top build cars which meet the emmissions-standards for the expected life of the vehicle.
I hope you did not pay for the 1st catalytic converter and you should not be paying for this one either.
Source: personal experince