I recently started experiencing this problem as well. The most annoying part of the problem was that the phone would shut down at fairly high battery percentages, like 14%, and then when I restarted it would be at like 2%, so clearly the battery calibration had gotten out of kilter.
I performed a full FDR last weekend, which did help overall battery life, but then I still experienced that early shutdown. So, I read somewhere that letting the phone charge from totally dead back to 100% before rebooting it would recalibrate the battery. I tried that earlier this week, and since then I can now get a full 15-16 hours from the phone with more than 20% battery to spare, and if I do need to run it down, it will get to single digits without spontaneously restarting.
I know that some will respond to say that you should never let your battery get below like 40% before charging, but most days that's just not feasible for me. I need the battery to give me a full day, then I plug it in at night to charge while I sleep.