that is probably not true. The heated sensors warm up faster, but they don't fail like the regular sensor does. they lose range and they don't always code like the one wire units. I would doubt it is bad, but less than 20 bucks will get you a good Denso sensor made for your cars.
If the o2 is bad, the car will run okay until it warms up and goes into closed loop mode.
As the car is acting like it is not getting fuel, I suggested turning up the pressure and seeing if there is a change in how it tries to run.
I think I also asked if you had looked at the bottom of the ignition module to see if it was gooey/melted which would be a sign it was failing. Maybe that was someone else