First please check that you have enough disk space. Do this especially if your host claims to give you "unlimited" disk space. Moreover please do check with your host if they have a limit on the number of queries you can run against the database. If it doesn't allow a burst of 100 queries per second for 2 seconds and a sustained average of 10 queries per second over 10 minutes the backup might, indeed, fail (since backing up the entire site requires making a lot of database queries to read all of the data contained in the site's database).
Assuming that these limits are not a problem let's try something that no host ever admits to but many of them do enforce: hard file size limits. Please go to the Configuration page of Akeeba Backup. Find the Archiver Engine row. Click on Configure next to it. A panel opens below. In there please set the Part size for archive splitting to 50M. If it keeps failing try lowering this to 20M, 10M, 5M, 2M, or 1M.
If this still doesn't help please reply to this ticket on our site. I will need to ask you for further information.
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!