I have witnessed firmware updates that fail to install when on secure corporate networks. In my case, the employer was running an SSL inspection tool that was causing Apple to not trust the connections and to drop the connections. Apple tests connections to ensure there is no eavesdropping and they also check updates are signed. Are you on a clean unmanaged Internet connection? Running the 'sudo softwareupdate -i -a --verbose' command from Terminal may reveal the portion that is possibly failing. It did in my case, a security update included a firmware update and it would re-install then fail with an error but only displayed the error on the command line. It may have been logged as well but who can find a needle in a haystack if you don't know what to look for?
Despite marking updates as ignored apparently it still triggers the notifications bubble on the Software Updates icon. So try a 'sudo softwareupdates --reset-ignored' command as well then check for updates again. I know it does this on Mojave as we made Catalina ignored but the notification bubble always comes back with no more updates to apply. It's a cosmetic bug.