I dropped my phone from only about 2.5ft, it must have fell on its side and the volume buttons took impact because they stopped responding afterward. Didn't felt like having to send it in for RMA, so I opened the phone. You simply need to use a T5 torque screw driver on the two bottom screws, then use something like a guitar pick to pop out the back cover.

The volume buttons are part of a separate thin board that also have 3 "gold clips" which will need to touch the contact points on main board in order to change the volume. When the volume buttons took the fall impact, the gold clips are squished so they are thinner and can no longer made the contact.

Nexus 4 - Simple fix after volume buttons stopped responding.-goldclips.jpg
Nexus 4 - Simple fix after volume buttons stopped responding.-n4volumecontacts.jpg

To fix it, I simply had to use a thin Phillips head or anything to stretch/widen these gold clips (carefully without breaking it). To get access to the gold clips you need to remove this separate thin board from the phone, in order to do that you just have to unscrew 9 screws to remove the inner black plastic cover that protects the board components, which hold this volume board in place.

LG design for the N4 volume buttons seems incredibly flimsy with these contacts, but at least its replaceable.