I see two possible problems. One is that your backup archive seems to be larger than 2GB. The other is that your computer seems to go to sleep or otherwise disconnect from the network after approximately 15'. Since both issues seem to happen within two seconds of each other I am not sure which would be the reason for the failure. So, let's address them both.
Go to Akeeba Backup, Configuration.
Find the Archiver Engine row.
Click on the “Configure...” button next to it.
Set the “Part size for split archives” to 2000 MB. You need to do that because your backup is beyond that size. Depending on how PHP was compiled, it may be unable to correctly handle files larger than 2GB minus one byte (that's not a random number; it's 2^31 - 1, i.e. the biggest positive integer which can be stored in a 32-bit variable because PHP can be compiled with 32-bit intrinsic integer size instead of 64-bit).
From the top of the page click on Save & Close.
Start taking a new backup. Make sure that you keep the tab running the backup active and that your computer does not go to sleep or gets disconnected from the network.
If the problem persists please check how much disk space you are using on your hosting account and how much is free. Since most of your site's content seems to be images, which cannot be compressed any further, you will need pretty much as much free space on your site as it's currently occupying.
If you are short on disk space and plan on storing the backups on remote storage please tell me which remote storage you'll be using and how much free space you currently have. There is a workaround for that use case. We can tell the backup to be broken into files smaller than 2000MB each and upload them as soon as they are ready.
If you have plenty of disk space do tell me how much space your site consumes, how much free space you have and give me a link to the new log file of the latest backup you took. There's a third, less likely possibility about what could be causing the backup to fail.
Nicholas K. Dionysopoulos
Lead Developer and Director
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