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I want to add that Dale's solution applies to files being uploaded to the server, not taking or downloading a backup. Re-reading the ticket I am not sure what the problem is but it seems that you have an issue taking a backup. I am not sure if you're saying that you are having memory, disk space or file size issues.

If you are running out of memory you need to change the memory_limit in php.ini. You need to consult the documentation of PHP and/or your virtual server's operating system for more information (e.g. the location of the php.ini file which varies wildly between different server setups).

If you have disk space issues you need to assign more space to your virtualised server's container. In this case you need to consult the documentation of your virtualisation software.

If you have file size issues you can set up a smaller "Part size for split archives" in the Configuration page of Akeeba Backup by clicking the Configure button next to the Archiver Engine row and setting a smaller "Part size for split archives".

This log file isn't helping at all. If you are sure that your problem is with the memory limit please follow my advice from the previous post:

If you are running out of memory you need to change the memory_limit in php.ini. You need to consult the documentation of PHP and/or your virtual server's operating system for more information (e.g. the location of the php.ini file which varies wildly between different server setups).

Since this is a server issue we can only tell you that you need a server level fix. The exact method is something your server administrator (your IT team?) should provide.