We understand that this is the fourth release this week and it can be annoying for our users. However, we considered it important to release it as it addresses two important issues, one of which could not be reproduced before as we didn't have access to an affected, misconfigured server.
The first problem resulted in a blank page or Internal Server Error 500 when you tried to access the component. This happens because a few hosts chose to disable a PHP feature called "tokenizer". This feature has been available in PHP for over a decade, poses no security threat and is in fact used by established PHP frameworks –such as Laravel– which are used for world class enterprise applications. We are as perplexed as you are why these hosts chose to disable this feature. We have worked around the issue by not using this feature anymore.
Side note: the tokenizer feature is used by all PHP-based template engines we've seen. If you are on an affected host it's more than likely that any kind of even remotely modern PHP software (CMS, e-commerce application, ...) will fail to load. In so many words, it's time for you to find a decent host with engineers who know what they are doing.
The second problem was entirely our fault and would prevent you from updating Joomla! when the "System - Backup on update" was enabled. Due to overambitious escaping of the output we accidentally converted ampersands in the return URL to an HTML entity, therefore causing the process to inadvertently loop forever. We consider any issue that prevents you from updating Joomla! to be priority 1 / security related. This is why we had to release this new version so shortly after the previous one.
We only support Joomla! 3.4 or later, including 3.5. We strongly advise you to run Joomla! 3.4.7 or later for security reasons. Older versions of Joomla! have known major security issues which are being actively exploited to hack sites. Please note that these security issues were fixed on Christmas Eve 2015 thanks to the effort of our development team who contributed their time and knowledge to make Joomla! secure.
Support for PHP 5.3 is discontinued. It's end of life since August 2014 and widely considered a security risk, unfit for production sites. Our software requries PHP 5.4 or later and is compatible with PHP 5.4, 5.5, 5.6 and 7.0. We strongly recommend using PHP 5.6 or 7.0.
We'd like to remind you that Joomla! 3.4 does NOT support PHP 7. PHP 7 is only supported by Joomla! 3.5.0 and later versions. Akeeba Backup will work perfectly fine (and very fast!) on a Joomla! 3.5 or later site running on PHP 7.0.