This problem is likely a battery issue as much as anything. The tech at Apple told me that upgrades sometimes reveal an underlying issue when the upgrade is installed. This certainly is our experience. Our battery was shot and failing which was why the battery indicator showed the phone rapidly draining with Sudden shutoffs. The battery and indicator were unstable and failing at below 20% reserves. I did the Factory Restore which allowed for things to come back to proper function for a time, but every time I put the backup of data back on the phone, the phone would start with the erratic behavior again. Apple ran their remote diagnostics on the battery. Mine was at less than 20% and failing.
I like the way you came back 180 degree to incorporate the battery-fail scenario I first hinted to you. There are surely several types of issues going on:
1- Battery drain, no sudden shutdown, good battery life (90+)
2- Battery drain, sudden shutdown, good battery life (90+)
3- Battery drain, no sudden shutdown, declining battery life (60-90)
4- Battery drain, sudden shutdowns, poor battery life (anything below 60)
5- No battery drain, sudden shutdown, good battery life
6- No battery drain, sudden shutdown, declining or poor battery life
Perhaps a patch can fix issues for those with Scenario 2, 5 and 6. What we do know is that continuous battery drain, or anything 1-4, = rapid discharge. Rapid mAh discharge kills Li-Ion batteries. Some readers dislike technical jargon, but it is reality. A leaking fuel tank will never get your car far.
Interesting that the PG technical data, plus facebook, or PG and Navigation are sufficient at 60% drain to reduce a Li Ion cycle life from 300-500 to 100-300 tops. I had no idea that Battery University folks were already studying the Killewr battery App scenarios..