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As far as site 1 is concerned, your host is forcibly terminating the execution of the CRON job exactly 7 minutes after it started. This is not enough time for a backup of your site to complete. Please ask your host to allow your CRON job to execute longer than that. How long? Exactly as long as it takes to backup your site (see the duration of your successful back-end backup).

As far as site 2 is concerned, you did not provide a backup log file. However we already know that GoDaddy imposes a CRON execution time limit around 150 seconds which is consistent with the output we see in your attachment. Again, it's the same issue. You need to ask your host to let your CRON job execute longer, so that the backup has enough time to complete on your site.

Please note that having one site successfully run a CRON backup on a specific host doesn't necessarily mean that all of your sites on the same host will have the same success. This depends on the size of the site (therefore the size of the backup archive and length of the backup process), post-processing options, disk/CPU/memory/database quotas per hosting account, differences in PHP/MySQL/Joomla!/Akeeba Backup versions among the different sites and so on. Therefore telling us that your other sites on GoDaddy can run a CRON backup just fine doesn't tell us anything in particular, except give us a hint that your other sites are probably very small and their backups complete in well under two minutes. I hope that clarifies my previous answers a bit :)