So it's later in the day now, no changes have been made since the previous posting. I gave it try again by just launching the old version and low-and-behold the download succeeds for the update - remember no changes were made. Then when you click the 'Install Now' in the next prompt it closes the application and nothing happens. It doesn't install the new version and relaunch the app. If you relaunch the app manually it's still the old version and not the new one you just downloaded and clicked to install. Ahh, this time I actually got output in the Console.app
Oct 10 16:31:54 Damons-MacBook-Pro.local Adobe AIR Application Installer[9129]: Application Installer begin with version 3.9.0.1030 on Mac OS 10.8.5 x86
Oct 10 16:31:54 Damons-MacBook-Pro.local Adobe AIR Application Installer[9129]: Commandline is: "/Users/damon/Library/Application Support/com.eworksmedia.xmpp.chat/Local Store/#ApplicationUpdater/update.air" 1.0.2
Oct 10 16:31:54 Damons-MacBook-Pro.local Adobe AIR Application Installer[9129]: Installed runtime (3.9.0.1030) located at /Library/Frameworks/Adobe AIR.framework
Oct 10 16:31:54 Damons-MacBook-Pro.local Adobe AIR Application Installer[9129]: Application Installer end with exit code 2