1.) Is this the internal update or installing the full downloadable version over the existing installation?
2.) What is the error message, if one is displayed?
From point number one the first workaround I'd try is downloading the full installed from Mozilla's website and overwriting the existing installation. Sometimes that alone cures the problem in the future while other times you have to investigate corrupt Firefox profiles and firewall settings. Getting the browser updated would be first on my mind, though.
Can't get firfox220.127.116.11 update to install, anyone out there have any ideas?