To the OP, if this one has battery problems, would you consider running some benchmarks to test whether it is a hardware or a software problem. I've been harping to people that random battery drain is not a hardware problem and will not be fixed by exchanging the phone and your case could be a good test.
download the app, "WPbench" available here:
WP Bench | Windows Phone Apps+Games Store (United States) when you have time to kill and run the battery test. This strains the CPU to max in order to drain the battery as quickly as possible. Since the CPU should already be at max capacity, any other program causing battery drain should not make any difference. Most people see times around 2 hours or so.
If the battery lasts 2 hours then any problems are software related and won't be fixed by exchanging the hardware. My pet theory is a rouge API that continues after the app that spawned it has been shutdown which is utilized by multiple apps (hence the many skype/whatapps/nokia drive/nokia trailers killed my battery threads). If its a rouge API, a simple reboot (not reset) should be enough to clear it.
Also, make sure to download and app like battery status
http://www.windowsphone.com/en-us/store/app/battery-status/e02e3a68-beba-493f-b000-e6e95281b444. This one shows the time remaining on even the smallest tile. If time remaining is greater than a day for a reasonable charged phone then there is no battery drain. If it drops to like 8 hours(with 90-100% battery left) once you've shut down apps and have allowed the program 10-20 minutes to requery battery draw levels, it may be time for a reset.
I really wish we had access to diagnostics like on windows phone 7 and 7.5. One of the options allowed you to see the actual current of the battery in realtime. It would be helpful in times like this. Here's what it looked like on my lumia 900.
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