Solution 1: Fail safe options
From v2.0.2, there is a ‘fail-safe’ mode during backing up.
First check [ ] Files and try backing up. If that also fails, check both [ ] Files & [ ] DB and try again.
Solution 2: If this doesn’t work, then
Increase the PHP memory and time limit by adding these lines to the .htaccess of your WP site
php_value memory_limit 256M php_value max_execution_time 800
Or edit these values in the php.ini of your WP site
memory_limit = 256M max_execution_time = 800