I've been struggling with this problem too. Battery percentages really can't be trusted. My 6p (running 7.1.1 DP) makes it to 15% then battery saver comes on ever so briefly then it shuts down. If I plug it in before restarting then the battery will still register incorrectly at restart. If I try to turn it on again right after it shuts down without plugging in, it won't fully restart, then I plug it in and restart, and only then will the battery show that it's at single digits when it restarts. I know it's not good to run the battery so low, but I'm a frequent traveler and just don't have a choice. If this keeps up much longer, I'm going to have to give up on the 6p.