I think this issue is caused by increasing demand of memory usage. If previously the backup was working, but not now after update or perhaps you have enabled some other plugins, it may hit the max memory allowed by your server.
You may make some tests. First I suggest you try to disable some (or all) other features of Better WP Security. Some reported File Change Detection usually consumes much memory. Also, you can try to disable some other plugins and then test the backup manually.
If after disabling some features or plugins, it becomes working again, it is very likely the cause is memory insufficient. You may ask your webhost company to increase the max memory allowed. Or you can google the web using keyword “increase website memory”, some webhosts allow users to manually configure the max memory via .htaccess or php.ini.
