2003 Pontiac Grand Am Catalytic Converter replaced, but cod

My state requires that you pass your emissions test every year on your birthday in order to renew your tag. (This is the case for most states right?). Last year I could not pass because my check engine light was on. The only OBD II code my car gave was P0420, meaning the catalytic converter was faulty. I paid $300 to have a new one put on along with an O2 Sensor and the light came off (I was told I had to get both of those parts changed). I went back for another emissions test, but the emissions people told me I could not pass because my car needed to go through a few drive cycles to make sure the light doesn't come back on. I drove around for a few days and the light never came back on and I eventually wound up passing the emissions test 3 weeks late. Unfortunately, about 3 months later my check engine light came back on and low and behold it was the same P0420 code for the converter. When I reset the codes, the same code would come right back on after about 10 minutes. The original mechanic will not give me a refund because he said I have not kept up with my tune ups which conveniently for him also cost $300. So now that it has been a full year again and time for emissions, I do not know what to do. Do I really need to buy a whole new converter again? Is it possible the wrong type of converter was put on my car? Can the code be coming up for some reason other than the converter or O2 sensor? It's so weird that the converter code came back up so quickly.