Before trying anything else, try these two things:

1. Quit NVDA (NVDA+Q, then exit), without shutting down your machine.
Does the exit sound play in that context?
If it does, then the suggestions about windows messing with the shutdown priority could be your issue.

If it doesn't, as I suspect, then you have a much more likely issue:

2. Try restarting with add-ons disabled.  You can usually do that from the NVDA+Q exit menu, although if you have that turned off, you will need to turn it back on (show exit options) in NVDA's general settings (NVDA+Ctrl+G).
Once you have restarted with no add-ons, try shutting down or just exiting NVDA.
If you get the sound then, your problem is an add-on.

 As I recall, there was a topic here a few weeks ago in which someone (David Goldfield?) had the same problem, and it turned out to be an add-on causing it, although I can't recall which.
Search the list archives for that.

Luke

 On Wed, 29 Jul 2020, brian wrote:

I have my nvda set to play start and exit sounds checked. When I turn my computer on I do hear the start up nvda sound but when I shut down my computer I don't hear any exit sound.  I have no way to know if my computer is shut down or not. I have only had this problem with nvda 2020.2