I also had the broken down volume button problem on my iPhone 5. Per the suggestion here, I applied pressure to the front top right corner while holding the phone and I was able to operate the down volume button.
I went to the Apple store for a more permanent fix, but was 3 weeks outside my warranty and was told it would be $200+ to fix. Or they suggested using the Assistive Touch floating button, but that is not very user friendly and I definitely did not want to spend that much to fix it.
I could see no noticeable bend in my iPhone 5 but figured since it works when the top right corner is "bent back" that the phone must have a little bend in it which is messing with the button sensor. So I built a little "jig" to put my iPhone in overnight to slowly / slightly bend it backward. I put a thin piece of foam under the center of the iphone and then clamped it down on both ends to slightly bend it. I was worried about cracking the screen, so did this very gently. Here is a photo of what it looks like clamped down. Note: it would be better to have something "wider" to clamp down on the iPhone as the small surface area of the clamp could damage the screen. I later usec a small, flat piece of wood to spread out the pressure from the clamp.
https://www.dropbox.com/s/jvgrvxaw4c9qlvd/Screenshot%202014-02-12%2014.01.54.png
I made sure when it was clamped down that I found the proper position to clamp the top of the iPhone so the down button was working. After sitting in this overnight, I took it out and the down volume button works fine. I kept it in this overnight for a few days just to be sure it did not slowly move back out of alignment. I've been using it for over a week now and it continues to work fine.
I am not keeping it in my pocket as much and am more aware when I am doing things that might "bend it" if in my pocket.
Anyway, just sharing a more permanent fix I found. I'm still disappointed that something as simple as the down volume button failed after a year and was held strictly to the warranty period. The down button had begun to work sporadically a couple months prior. Lesson learned... if anything is wrong with one of my Apple products no matter how minor, I willl be bringing it in to be fixed / replaced ASAP.