My 5 does this from time to time too. What I found on a site and it may have been here when I used to lurk was let it shut down. Not sure if it applies to the 6 Plus as I am still waiting for mine.
So let it shut down.
Plug it in the wall and as soon as it comes up unplug it and do a hard reboot (Top and Home Button until Apple logo comes up.) then plug it back in and don't touch it for four hours. Sometimes I had to do it twice but now my phone goes all the way down.
AGAIN that was the 5 and this didn't start happening for about a year and a half so you may want to bring it to the Apple store to have the battery checked. Not to mention that process may not even apply to the new phones. Not sure but just wanted to mention it.