Apparently there is a thing with the iPhone not liking to be charged while in a case and also not liking to be in a case.
While I was in Dallas this weekend I made an appointment at the Apple Store to discuss my short battery life. They kindly asked me some questions about how I use the phone and whether in a case or not and then how I charged it. They gave me some suggestions, including not charging while in a case. They also deemed that my power brick was faulty.
After about a half hour of discussing it, they told me to follow their suggestions and if that didn't work, to bring it in and they would send it to be fixed. That was really kind of them to offer to pay for me to drive all the way back to Dallas in order to drop my phone off. How amazing of them.
No, wait. That isn't what they said at all. They said that I could come back, when I told them that I lived 5 hours from that store, they told me to go to a closer store.
So far, amazingly enough, the battery is doing well without a case.