Your log file never made it. If it's more than 2MB please put it in a ZIP file and attach it. If the ZIP file is also bigger than 2MB please upload it to a public location and give us a link.
That said, I think I can help you by guessing what happened. Try using a small part size, e.g. 5MB. If that still fails the problem is not the part size but something on the server. If you see the upload starting in the log file but never finishing the problem is a firewall on your server preventing access to Amazon S3's servers. You will have to ask your host to fix that issue (it's not under your or our control).
If you see a few upload steps going through but the last one of them never finishing try decreasing the maximum execution time in your Akeeba Backup Configuration page.
If that fixes the issue go back to the Configuration page and set the part size to something big, up to 2047MB. Then on the Upload to S3 configuration make sure that "Disable multipart uploads" is NOT checked. This tells Akeeba Backup to upload files to Amazon S3 in 5MB chunks and then asking it to stitch those chunks back together in one big file. This is the preferred method instead of decreasing the part size of the backup itself. It just has the drawback of using more space on your server before anything is uploaded to Amazon S3.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!