Suggestions to help diagnosis an idling problem

TheBuster

2011 370z with ~57,00 miles

I have had this car since it was new. It developed an odd idling issue this week. I take two 15 minute breaks and a 30 minute lunch in the car each work day. It is warm enough to start the car and run the AC.

On occasion the car has a hard start but generally no issue starting. Once or twice it cranked and tried to start but took another attempt before it fired up. After is is started and running I detect no issues. After about 3 minutes it starts dropping idle, misfires, sputters, and attempts to die until the engine eventually cuts off. By the the noises it's making and the vibration sitting in the seat it feels like several cylinders are misfiring.

Once this erratic idle starts if I manually fast idle to car to 1500 it's fine until I let off and let it idle normally. But one or twice trying to use the throttle did not work similar to limp mode, push the throttle and no response.

If I put the car in gear and drive it, I have absolutely no issues unless I stop and let it idle for longer than 3 minutes. The car drives normally as long as I am moving and not idling.

I have a gauge under the hood and it shows a steady 58 lbs of fuel pressure even when this erratic idle starts. It has not thrown a light and I have no pending codes.

What should I start looking at? Like I said the car runs well as long as I am driving it.

Thanks for any direction on what to troubleshoot.