Did cpanel backup to ftp with no problems - to check the hosting...
This is an irrelevant test. cPanel's backup runs as a system process with no CPU usage / time limit restrictions. Akeeba Backup is a PHP script which runs with CPU usage and time limit restrictions. Moreover, since Akeeba Backup is running inside your web server it is also possible that there are additional restrictions to which external servers it can contact, restrictions which do not apply to cPanel's backup (because that one is running as a system process, of course!). In other words what you did is like driving your car to make sure that the sea is not too rough for a boat ride. It doesn't make much sense and doesn't give you any other insight than knowing that cPanel's backup works.
Regarding your FTP transfer I see that you have a single file which is 142308328 bytes (135.72 Mb) big. It is too big. Why? It's what I explain in the Basic Configuration section of the documentation:
PHP always has a strict time limit, i.e. the maximum time a PHP page may process data before the web server aborts it. Uploading the backup archives to cloud storage takes time, the exact amount of which depends on the size of the file and the network speed. The time limit and the bandwidth are beyond our control, so we can change the only parameter we can touch in order to avoid timeouts: the file size. Akeeba Backup Professional is smart enough to upload each part of the backup archive on a PHP page load of each own, so as to avoid timing out.
So, you just have to use a Part Size for Split Archives in the area of 10-20Mb. This will split your backup in 7 to 14 files with extensions .jpa, .j01, .j02 and so on. Each one of those smaller files can be successfully transferred.
If this doesn't work you will have to contact your host and ask them if there is a firewall blocking connections to external servers from inside a PHP script.
Nicholas K. Dionysopoulos
Lead Developer and Director
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