Phone Dies Before Battery Shows 80% topic

I have been loving my Nexus since I got it on the first day it was available, but a couple days ago it started acting very odd. The phone will intermittently "die" while the battery is still mostly full. The phone will shut down, and if I try to restart it the screen displays the empty battery symbol and will not boot. As soon as I plug the phone in, though, it will boot up immediately and the battery charge icon while the phone is off shows as almost or completely full. When I boot the phone back up it looks like it has 90% or so.

Has anyone else seen this issue with the N6? The phone is completely stock 5.0.1. I purchased it through Sprint, but as far as I know it's exactly the same as all the rest of them.