I have managed to edit the Registry so as to get the Windows Installer (MSIExec) to write a verbose (detailed) log. From this, and some web forums, I found that the problem has been caused by a Microsoft Windows security update, KB2918614. This was applied on my PC on 14 August but I think it was released on 12 August. My Windows version is Vista and I don't know if this update or a similar has been applied to other Windows versions.
For more information see wix-users - SECREPAIR: CryptAcquireContext: Could not create the default key container.
I went into Windows Update on my Control Panel and found how to uninstall update KB2918614. When I had done this, followed by a Restart, I was able to install AIR and the software that uses it.