I was wondering why I can't replicate this issue, until I looked closely at your PHP version: 5.2.17.
It turns out that Akeeba Backup 3.6.0's System Restore Points feature is not compatible with PHP 5.3 and I never tested it with PHP 5.2 (I only tested full backup scenarios with PHP 5.2). The incompatibility was introduced due to the changes I made to make the component compatible with the upcoming Joomla! 3.0. I have good news, though! It seems that there is a workaround. Please download and install the latest
dev release. Don't freak out because it's listed as alpha; it's very stable. The only changes since 3.6.0 are the bug fix in question and a CSS fix for the Live Update icon floating behind the right-hand column in Akeeba Backup's Control Panel page.
In order to test the dev release please disable the "System - System Restore Points" plugin and install the dev release on top of your existing version. Then re-enable the "System - System Restore Points" and try installing another extension so that you trigger the system restore points. The SRP backup should complete successfully and the extension installed.
Nicholas K. Dionysopoulos
Lead Developer and Director
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