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Akeeba Backup DOES NOT perform the update. The only thing it does is download the installation ZIP file. Then it calls JInstaller, the Joomla! extensions installation class (which is part of Joomla! itself) and asks it to install the package file. It's the same thing as using the Upload and Install method. Besides, you just said that the files are there, but have zero size. There is exactly one way this can happen: corrupt filesystem on your server (your site's server crashed). Unfortunately, the only workarounds are asking your host to restore your files (if they have backups...) or restore one of your own backups. This is why I am telling folks to keep off-site copies of their backups.

In any case, this is not a bug in Akeeba Backup as it never had the chance to run and do anything to your site, not to mention that the update can not write to all files and all folders in your entire site during a single page load (it would take 10 minutes to do that and you'd see an error page long before that would conclude).

You seem to have used Joomla!'s extension updater, not Live Update which is included with our component. As mentioned in our release announcement:

DO NOT USE JOOMLA! 1.6/1.7/2.5's EXTENSION UPDATE TO UPGRADE AKEEBA BACKUP. The Joomla! extensions update was never designed to update component which need to supply authentication credentials to the download server. We have applied a workaround, but it's still in experimental stage and may not work properly. At best, you'll just get an error message. At worst, you will not be able to access the Manage Extensions page, in which case you'll have to remove the plugins/system/plg_srp directory

Maybe, and I stress maybe, using Joomla!'s own updater without having provided a Download ID in the component can cause this problem. And I repeat, that this is a huge MAYBE. I will have to try to debug JUpdater, which isn't exactly an example of clean and stable code. It will have to wait till I get back from Joomla! Day France, though.