Firefox latest version is 44.0.2. So please update it :)

Please see this KB article - How can I get the latest version of Firefox on Windows XP or Vista?

There is a server security issue with Firefox versions above 43.0.1 that started as of 01-02-2016 with regards to both WinXP and Vista without the correct Security fix from Microsoft, where users can't install a version after 43.0.1 directly, but need to update Firefox thru the Firefox updates system to have the newer versions.

The "fix" is available for Vista with SP2 here: https://support.microsoft.com/en-us/kb/2763674

WinXP users are SOL, as Microsoft ended support for XP close to two years ago.

You should get a update to 44.0.2 from a 43.0.x version. If you were downloading from mozilla.org then that would explain the 43.0.1.

The problem is not every Visa user keeps their system updated so as to have SP2 and patches like the kb2763674 installed.

WinXP users who have SP3 can install the newer Firefox setups since 43.0.2 however those still using SP2 cannot.

The web brower UA's does not show what SP they have and whether they have certain patches installed. So Mozilla chose to serve a working setup version to WinXP, Vista (also 2003+2008 server) users that they can update from instead of a version they may not be able to install.

Thanks to all those who replied. The root of my problem with Firefox updates was, in fact, problems with my Vista upgrades. While those problems turned out to be more involved ("fun" with corrupted upgrade registry entries), I am now running Firefox 44.0.2 on a fully updated Vista machine. ;)