We seem to keep having cycles of "the update issue" which is well known, and already solved, popping up again and again. I am hoping this Admin Notice will help those who might encounter the issue to fix it just from having read this message. Please file this if you are using NVDA 2021.1 or 2021.2 (or even some earlier version of NVDA) as you will almost assuredly need this information.
The update problem is cause by a certificate issue and a Windows-based certificate. It is not a problem with NVDA, per se, but something that NVDA is seeking from Windows when trying to update. This issue is fixed, permanently, with NVDA Version 2023.1. The current version of NVDA as of this writing is 2021.3.1.
You cannot fix this problem by trying to update/upgrade from within NVDA, as that's the part that's broken. You MUST download the latest version of NVDA from NVAccess and use that installer. For NVDA 2021.3.1, the direct download link for the NVDA installer is:
[As an aside, if you're ever looking for an older version of NVDA, just change the "2021.3.1" in both places in the URL with the version number you want.]
After you have the installer in hand, you can either uninstall the current version and then run the new installer (preferable), or do an install-over install by just running the new installer. Both have worked in my experience, but the former is the one that ensures you are "clean as a whistle" before going forward.
If, by chance, you really need to be on a version of NVDA that is prior to 2021.3.1, then you can reinstall it afterward, and the issue that was causing the update to stall previously will still be fixed, as it is fixed by the certificate tweaking that the installer for 2021.3.1 does in folders not belonging to NVDA. You can use the download link given above with the release number changed to the release you want to get.
Brian - Windows 10, 64-Bit, Version 21H2, Build 19044
The instinctive need to be the member of a closely-knit group fighting for common ideals may grow so strong that it becomes inessential what these ideals are.
~ Konrad Lorenz (1903-1989)