Following the Xamarin on-screen notification that there was an update to the Studio, I accepted and the download and installation started - then failed. It appears that the cause is:
"Error 1303. The installer has insufficient privileges to access this directory: C:\Program Files (x86)\MSBuild\Xamarin\Android. The installation cannot continue. Log on as administrator or contact your system administrator. Action ended 09:28:20: InstallFinalize. Return value 3."
I would think that the installer should request these privileges BEFORE it starts rather than CRASH the process.