With my 1995 I had the same symptoms. But the 1995 would eventually set a code saying the O-sensor was bad.
What had happened there was I had made the cats freer flowing (IE: Gutted) but since the passenger O-sensor was right near the cat, since the cat was now gutted it didn't keep the o-sensor hot enough so the thing would read slightly lean, the computer would richen it up, then it would start clogging over time and a dominoe effect would occur where the car would keep richening, making the o-sensor clogging worse until it eventually wouldn't read anything.
So I would think that two things I would look for on your car is:
1. Faulty O-sensor (oxygen sensor)
2. A leak in your exhaust somewhere between the engine and the oxygen sensors that might be allowing fresh air to get in there, which would cause a false lean condition and make the car richen up.
I would lean toward the latter, because if the o-sensor was bad the PCM would probably report it, but who knows?
-Dave C. '04 Z06