nexus 7 volume keeps muting At completely random times the on screen volume slider appears and mutes the sound. Also the slider just stays on screen over anything I'm doing (as it is now) and will not disappear. Sometimes touching the volume rocker switch will work, often it doesn't. So even if I don't need any sound the slider is on screen interfering with whatever I'm trying to look at.

Rebooting doesn't help. This occurs whether any apps are running or none and there is no way of telling when this will happen.

Also if I do want to listen to something the slider will just appear and return to mute, so if I try to turn the volume up with the rocker switch it just immediately slides back to mute.

It's happening more frequently, pretty much all the time now. I had hoped the recent KitKat upgrade would resolve it, but no luck. I have taken it out of its case so there is nothing pressing on the buttons. This is the old style nexus with one camera.

What could cause this, and how can it be solved?
As said in the comments it looks like your volume button could be broken. A good way to check if this is the case is to disable it. There are some great threads on how to do this so I will list a few here that you can check out. If the case is that the button is broken, let me know in a comment (on this answer) and I will help you out.

Threads:

http://forums.androidcentral.com/lg-optimus-g-pro/284907-how-disable-side-volume-buttons.html

http://androidforums.com/droid-support-troubleshooting/33602-disabling-volume-button.html

http://forum.xda-developers.com/showthread.php?t=2125810