My keyboard is a Logitech Illuminated Keyboard K740. It has mute, volume up, and volume down functions that are not working in game (or within any game menu's)

Was suggested it was because of the windowed screen, but had no effect. Tried Fullscreen, Windowed, and Borderless, these buttons are not working. Cannot remember the last application in which they did not work.

Any help would be appreciated.

Same here, I'm unable to change the volume using the scrollwheel on my keyboard (Logitech G710+).
So far only one other game hasn't let me change the volume while in-game and that was stalker (and all the follow-ups). :o
If I want to change the volume I have to alt-tab out of the game. But since it crashes so often I don't dare to alt-tab just in case it might crash/freeze again. :(

Did you install a new Nvidia driver prior to playing W3?

I'm on the latest driver from Nvidia but even the one prior to that I wasn't able to control the volume. :(
And I'm betting that even if I plug in my corsair K90 it still won't register the volume adjustments.

Well, I was curious if you had noticed a windows compatible device being installed alongside when you rebooted.

I thought I noticed something when I did, and I never check the box next to HD Audio device in the install process.

I just installed the bare driver, no other software (that means no audio drivers, no gefore experience and no physx).

I can't believe this issue still exists in Witcher 3. I have a Corsair gaming keyboard with a volume knob and previously had a Gigabyte one. Both previous Witcher games had this same issue. The only way to control the volume was to swap out of the game first. Like you, I can't remember the last game I had this issue with. In fact, I don't think I've ever had it with a non-Witcher title. I really wish they'd fix this bug for good.

Any hope of getting some dev comment on this?

I would try at cdprojektred.com forums, but can't even register there.

I am having same issue with my Microsoft Wireless Keyboard 800.