I'm having problems with my battery life too.
When I first got my 6+ I would go 16 hours of mixed usage (music, mail, text and web) and end up with about 70% left.
I used my phone camera heavily one day last week, draining the battery completely, and since then I've been seeing it completely drain to 0% in that same time with the same use.
I've cleaned up background apps, closed all unneeded apps, and reboots. No love.
I've even tried a battery reset by draining it all the way, leaving it that way for a few hours and then charging it all night. That fixed the problem for about two days. Now its back. My app usage is showing lock screen and mail taking up 50% of my battery. I've also set my email to only synch manually.
I'm at a loss. I'm thinking its a software issue. I've had a battery go bad on my iphone 5 and it behaved differently. That one would die with 30%+ battery showing and stuff like that. So, I'm still searching for the fix. If I figure it out I'll post it here.