I stopped by the Apple Store earlier today. The guy at the Genius Bar told me that they've had a few people come by with this issue, and that the store has escalated the issue and notified Apple. He believes that the next software update will solve the problem. If it doesn't, he said I can come back and swap it out no problem. He also said that he'd swap it out for me right now if I'd like, but there's no guarantee that the new phone won't have the same issue.
I decided to hold on to my current one and see if the problem persists after the update.