Sorry I did not update this post. The phone went to Texas and back in under the 7 to 10 business days they quoted me. Same phone as I sent in. I don't know if they changed the guts, but the chasis was the one I sent in. Phone works, but was wiped to factory new.
The issue still seems to be netflix. It appears that the Netflix app disables the power management system. I think it even disables the charging system. I mean the phone should be able to draw enough power to charge and run the hardware at the same time.
To recap, I was watching a Netflix movie when the battery died. The phone then refused to charge the battery.
Two nights ago, I was watching 'The IT Crowd'. I had watched two episodes and decided I should check the battery before starting a third. I did not want a repeat of last months death. I exited Netflix and checked the battery indicator. It showed slightly more than half full. I watch about 10 more minutes of Netflix when the phone went dead. I thought 'SOB, not again!' I put the phone on the charger and it looked like a repeat of the last time. The 'LG' screen came up and just sat there. The phone was pretty warm (not really hot) so I just took it off the charger and left it for the night. When I plugged it in in the morning, it displayed the 'LG' screen for about 60 seconds before displaying the dead battery charging screen. About 5 minutes later it booted to the main screen.
This makes me think that Netflix is disabling the power management system and the phone is not aware that the battery is getting critically low. The fact that this can happen when the phone is plugged in makes me think that even the charging system is disabled by the Netflix app.