Code P0420 keeps coming back?

Hello, you could be getting that code for a couple of reasons, the engine computer (ECM) monitors the front oxygen sensor and the rear one (after the Catalytic converter) and compares the frequency or switching time of each. When the sensors start to display a signal that is close to each other it will set that code. The rear oxygen sensor should have more of a steady reading because a converter actually stores oxygen and uses it to help burn off extra emissions. I'll post some other possibilities that can cause the code, but if the vehicle is going into limp mode, it is doing that to protect the converter from damage. So misfiring cylinders is what will cause a converter to melt down and fail, eventually it will melt and block off the exhaust and the vehicle won't start at all. If you're getting any misfire codes, you need to get them fixed. Converters are very expensive. But next time you get a check engine light make sure to write down all the codes, If your scan tool can look at live data, look at the rear oxygen sensor data. It should have a steady voltage signal. It's only a 0 to 1 volt switch, but it shouldn't be swing up and down.
If the main issue isn't fixed it will only get worse and leave you stranded eventually. I'll post some more info on that code.
And just one other thing, since this is a V8, the p0420 is only a Bank 1 code, so it's one side of the engine causing this code, the Bank 2 would be a P0430. So, you might have cylinders misfiring on just the Bank 1 side.

On a side note, I did find 3 Recalls, the first 2 are for the Fuel Rail pressure sensor not being torqued to spec, but the 3rd is a Recall of the sensor itself, this is something you'll want to see if it's been done or not, You don't want any fuel leaking out of the fuel rail. That could be a fire hazard besides a performance issue.

https://www.2carpros.com/articles/bad-catalytic-converter-symptoms

The converter needs to be able to store oxygen to do its job, your mechanic is referring to when the converter gets to the point of no return, when it melts down and breaks apart it will clog up the exhaust and that entire bank that the converter is on will not be able to allow its exhaust gases out, when it can't allow anything out, it can't take anything in either. So, air flow is restricted, cylinders start to foul out, all kinds of bad things happen. When you're clearing your codes out, it's clearing the memory. Modern vehicles will sometimes disable fuel injectors when there is a cylinder misfire code, or any other code that has converter damaging effects. The ECM will do what it has to when trying to save the converter from damage. And yes, it will affect fuel trim numbers, when the rear oxygen sensor starts to become active and its frequency/switching time is reaching what the front one is doing, the ECM will reduce fuel and the long term and short-term fuel trims will start to go negative, meaning taking fuel away, again to prevent converter meltdown. The mechanic doesn't care, because then he gets to sell you a $1,000.00 converter, or whatever the price it is for your vehicle. I can't imagine they are cheap for an Infinity.
But monitor the rear oxygen sensors and see what they are doing and write down any misfire codes or any other codes you get next. You also want your fuel trim numbers to be less than 10percent negative or positive. Over 10 is no good. That's too much compensation.