Makes no sense at all to me. Check the wiring and the plug connection. If those look good, I'd suspect that the sensor is no good. Did it have a little paper spacer on it? That's there to assure clearance is proper.

 

I will run live scans today later. I also found out the O2 sensors have a total of 4 on this car = 2 before cat & 2 after. That just dont make sence to me either?? Never seen that before -I also will check for fuel pressure & fuel pump running after the engine dies also. On scan & by ear @ tank!--- Years back I had a car that did exactly the same - was a computer then too. Yet here i also have a olds V6 that did same & was a crank sensor too- replaced that & ran fine - both cars didnt toss any codes either!! Go figure!

 

it's a v6; each bank of cylinders (3) has a pre cat O2 and a post cat O2.

2+2=4

 

now you are referring to MILEAGES at which it shuts off.
before you were referencing TEMPERATURE (when it warms up) it shuts off
You're giving us apples and oranges to compare, which is not only confusing but helps none of us get any closer to solving the issue.

Try this: Let the car warm up idling in your driveway with the scanner attached.

Capture real time data for the coolant temp sensor, CKP (crank Posit Sensor), and CPS (Camshaft position sensor), Fuel pressure, Front O2 readings.

Do NOT stop taking data when the car shuts down; go for another minute and monitor all the same things.
_______

Aftermarket sensors, depending on type, may be ok, and sure cost less than OEM sensors....UP FRONT. When you add up all your time messing with them + the cost of an OEM replacement, it costs more.........