Linux Mint gets the most complaints about Grub not updating but it is not really a Mint problem. The volume of complaints is due to the fact Mint is the most popular flavor of Linux.

The other reason is so many people install Linux on older hardware. This is another example of why Agile is not now, nor will it ever be Software Engineering. Your Jenkins automated testing doesn’t test squat.
Here is the real problem
In case you cannot see the featured image.

Sorry about the phone camera flash. You can still see what is important. It is that 1 MiB BIOS Boot partition. I originally installed Mint on this 1TB SSD when it was in a really old AMD 6-core computer. Like the computer moved the drive to, it can, but it does not default to EFI boot. One has to change the BIOS settings. When I replaced the battery on the Mobo, that was one of the settings I missed changing back.
You see, Mint (and probably most other Linux distros) the hardware wants a standard DOS boot. So, that 1 MiB BIOS Boot partition gets created with just enough code to launch the EFI partition. The typical end user thinks the machine booked from UEFI because that’s what it looks like.
Grub no like it
The Grub update process is poorly tested. Yes, I’ve given you Grub hacks before, but this isn’t a Grub hack. If you are dual booting Windows XP or some other gotta have a DOS boot OS, all you can do is file a bug report. The Grub update process that runs as part of the graphical software update looks at the BIOS Boot partition expecting UEFI and can’t figure it out.
Adding insult to injury, if you open a command line and do a
sudo update-grub
it works!
If Linux is the only OS on your hardware, then you need to search online for how to get into the BIOS and what setting to tweak so UEFI booting, not “legacy” is the default. Once you have that set, reboot, wipe the drive, and re-install. When you check the drive that odd little BIOS Boot partition won’t be there. Updates will work because you now have the only path that was ever tested.