https://support.mozilla.org/en-US/kb/how-to-fix-preferences-wont-save

Note: Some software, like Advanced SystemCare with Surfing Protection, can protect files in the Firefox profile folder against changes. If you have such software then check the settings or uninstall this software.

If the above does not help;

Let’s do a full clean re-install;

Download Firefox For All languages And Systems {web link}

Save the file. Then Close Firefox.

Using your file browser, open the Programs Folder on your computer.

Windows: C:\Program Files C:\Program Files (x86)

Mac: Open the "Applications" folder. https://support.mozilla.org/en-US/kb/how-download-and-install-firefox-mac

Linux: Check your user manual. If you installed Firefox with the distro-based package manager, you should use the same way to uninstall it. See Install Firefox on Linux; https://support.mozilla.org/en-US/kb/install-firefox-linux

If you downloaded and installed the binary package from the Firefox download page, simply remove the folder Firefox in your home directory. http://www.mozilla.org/firefox#desktop ++++++++++++++++++++++++++++ Look for, and remove any Mozilla or Firefox program folders. Do not remove the Mozilla Thunderbird folder if there is one.

Do Not remove any profile folders.

After rebooting the computer, run a registry scanner if you have one. Then run the installer. +++++++++++++++++++++++++++ If there is a problem, start your Computer in safe mode and try again.

http://encyclopedia2.thefreedictionary.com/Linux+Safe+Mode This shows how to Start all Computers in Safe Mode; Free Online Encyclopedia

Your Firefox reported itself to be the "beta" version, which definitely gets more frequent updates than the stable/release version -- probably 13 so far. But I don't think it should update every single time you exit the browser and start it up again.

If the clean reinstall doesn't help -- and I think you might be looking for the beta again, from

https://www.mozilla.org/firefox/beta/all/

-- then you could check for an update folder that isn't getting cleared out as expected.

Paste the following shortcut path into the Windows search box or the address bar of Windows Explorer, and then press Enter to load it:

%LOCALAPPDATA%\Mozilla\updates

That should expand to the hidden folder:

C:\Users\your_username\AppData\Local\Mozilla\updates

Here you normally find folders with log files for past updates, and folders for any staged updates that will install on your next Firefox restart. If you see any folders with files to install, go ahead and remove them. Firefox will check for updates again tomorrow.

Thank you all for your help. It is good now.

As a 'me too' response, I too have had this irritation (not a problem as such) for the last week or so. Even restarting FF generates this update warning from Windows, and FF says that it's installing updates. I've looked in the folder %LOCALAPPDATA%\Mozilla\updates as helpfully suggested above, and there are two logfiles: backup-update.log and last-update.log. The time stamp on the latter is changed on each restart as you'd expect from the name. This has a lot of PATCH lines, interspersed and appended by what look to be error messages, eg:

FINISH PATCH AccessibleHandler.dll backup_restore: backup file doesn't exist: AccessibleHandler.dll.moz-backup

The general tenor of the "can't do this" errors seems to be a permissions problem.

I'm not bothered about fixing the irritation as it only costs one click on a Windows alert to dismiss it, and arguably it's not worth even writing this message. I'm definitely not going for the default 'reinstall FF' option just for an irritation, but I am curious as to why this has happened in the last few days. I've not changed the machine or FF config in that time, so I'm guessing that it's been provoked by some tweak at Mozilla Towers.

It's really, really not any big deal. It's not even a small deal, or even a nano-deal.

Have you tried a full clean re-install; https://support.mozilla.org/en-US/questions/1227920#answer-1138971

Ah, well I did write that I wasn't after a scorched earth solution:

"I'm definitely not going for the default 'reinstall FF' option just for an irritation"

I know that a reinstall costs an hour or two or more, whereas a single click when FF starts costs just a second. I'm not after a fix as such, I'm just curious as to why this might have just started happening with my copy of FF. No bother, I'll put up with it, it's not a problem. FF continues to be the dog's bollox of browsers :o)

A reinstall would solve the issue if any of the program files were corrupt.

Firefox comes in two or more folders on all computers. They are;

Maintenance: (Programs Folder) <Windows Only> Firefox itself: (Programs Folder) And two folders in the profile of each user on the computer for each Firefox profile for that user.

If you remove the Firefox folder, the user profiles would not be affected.

FredMcD said

A reinstall would solve the issue if any of the program files were corrupt. Firefox comes in two or more folders on all computers. They are; Maintenance: (Programs Folder) <Windows Only> Firefox itself: (Programs Folder) And two folders in the profile of each user on the computer for each Firefox profile for that user. If you remove the Firefox folder, the user profiles would not be affected.

Thanks for taking the trouble to reply, Fred. I will bear the above in mind if FF behaves badly/weirdly in the future. I doubt that there's a corruption with this issue, more likely a particular update flag's not been set correctly.