I am having this same issue. I have seen a couple of threads on Apple and Macrumors about people dropping their iPads and this issue, but this is the first without dropping.
I did not drop mine or do anything else unusual. There are no dents or even scratches on my case. I keep itin a leather book style cover all the time and use a padded case when I take it anywhere.
It was working perfectly, had it since May. Now suddenly the up volume button does not function. Down works fine. I went to Settings first and found that though I hadn't changed it, the selection for physical volume buttons was set to no. I turned it back to yes, hoping it would solve the issue, but no luck.
I rebooted and then the volume was back at full, but the icon would not fade from the screen. When I pushed up, nothing happened. When I used the mute slider, the icon flashed the mute icon, but wouldn't stay muted and the icon remained. When I pushed down, it worked as usual and the icon finally faded, but up won't bring it back and doesn't increase the volume.
I did another reset with both the power and select button (instead of just the power button). Again, when it came back on, the volume icon appeared immediately (it doesn't normally do this) and raised itself from all the way down to all the way up and the icon "stuck" there on the screen no matter what I was using, such as Safari, email, FB app, etc. the only thing that made it disappear, other than using the physical down button, was going into the Sounds section of Settings. Once I exited Sounds though, the icon reappeared and remained stuck until I pushed the physical volume down button.
Since there is not a slide volume available on everything, this is a huge issue. I will probably end up at the genius bar, but I HATE having to reload all my stuff. Apple has great service, but I dislike that they swap you out, sometimes with loss of data, and there is never any public acknowledgement of known issues or fixes announced.
Sorry for the rant. If anyone happens to have a suggestion for a trick that might reset this weirdness, I would love to hear it. Thanks!