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Your backups fail because your host is imposing a maximum CPU usage time limit. Please note that CPU usage is different than wall clock time, hence the small variability of a few seconds you may observe in different backups' log files from the start of the backup until the point it abruptly stops.

You will need to contact your host and let them know they have to make a configuration change in their server to let you run your backups. You may use the following text, replacing XYZ with the time it takes to run a backup from the backend plus about 10%. You can find out the time it takes to run a backup in the backend of your site, Akeeba Backup, Manage Backups. If you have multiple backup profiles use the time from the longest-running profile.

Here is the text to use:

I am using CRON jobs to take a backup of my site. I have observed that my CRON job stops executing at around 360 seconds. This is not enough time to complete a backup of my site. This means that you have set up a CPU usage limit either with ulimit or the /etc/security/limits.conf file on your server.

Please make the current CPU limit for my user into a soft lift and set up my CRON jobs so they have a CPU limit of XYZ. This would allow my backups to run without affecting the sensible time limits you have set up for PHP script running over the web.