While these are good pieces of info, they don't necessarily point to a root-cause of the problem. Whether the device is optimized or not, shutting down while the battery gauge shows 1/3 or more available power is bad.
Possible issues:
- The battery gauge is actually wrong and you don't have as much power as you believe you do. Use the Battery Life app to compare what IT sees versus what YOU see from the gauge in the status bar.
- The battery is actually bad INTERMITTENTLY. It may work fine some of the time while others it fails. This could be heat-related in that the battery might experience an internal short when it's very warm. Making sure that you don't have apps running in the background using battery (CPU) would be wise.
- An internal short in the phone somewhere could be causing an issue, although I suspect this would more likely cause the phone to restart than just shut down.
Go into Settings -> Battery and look to see how much of the CPU is being consumed by various apps. Tap the clock symbol on the right side at the top of the app list to see actual amounts of TIME that the various apps are running for. This should give you some insight into what's using the most power and a rogue app in here could enlighten you to what's going on.
I agree with Meg on the notion of going BACK to the Apple Store and talking with a manager. Explain the situation, and be prepared to DEMONSTRATE it. Their tests are good, but they will not necessarily re-create specific conditions that would cause the phone to actually shut down.