There's actually a class action lawsuit related to this issue [1]. I first read about it here [2]. I've got a Nexus 6P too and it's great except for the battery and shutdown issues. Mine will shut down at like 20% or so so it's very usable, but it's often at night when I most need to use my phone (calls, rides, etc).
Despite the comments there about software it is most likely about heat and a component which is affected over time.
I've had a 5x just go dead. Bought a Pixel, it died after a week (probably unrelated to this fault). The replacement is fine though and the phone is great overall and the camera is fantastic.
I really cannot understand why consumers persist in buying smartphones with non-removable batteries. All of these battery degradation problems are reduced to minor annoyances if you can buy a replacement battery for ~$35.
I called Google (bought it from the play store), they asked me to try a couple of things in order to repair the phone (completely useless but the operator has to follow the script).
Of course it made no difference, but just after confirming that, they sent me replacement device.
Google replaced my 6P a few weeks ago, it was also shutting down early. It was months out of warranty (bought at launch) and they made me take lots of pointless steps like running in safe mode and doing a factory reset, but the process was straightforward.
Also if you're in the EU remember you have a statutory 24 month warrantee for non-consumables. (The standard example of the sort of thing not covered is an oil filter which is expected to have a shorter life)
Thanks - I actuallly bought from newegg so Google store didn't want to help. I rang Huawei today who I think are about to replace or repair it so hopefully I'll have a working 6p again soon. Maybe the lawsuit helped as previous comments I'd read gave me little hope. Huawei support is 1 888 548 2934 in case anyone else needs it.
The main problem I have is that it shuts down after 10-30 minutes of use - no help from google. https://code.google.com/p/android/issues/detail?id=227849 Makes me want an iPhone. (see below Huawei might be fixing)