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The error message means that the server killed the execution of a database query. That would make sense if it was a very slow query, but we're talking about a query that takes less than 0.1 seconds even with ten thousand backup attempts in the database.

Most likely something is broken in your database. First try going to Components, Admin Tools and click on Repair and Optimise Tables. When it's done, go back to Components, Akeeba Backup.

If you got errors during the repair and optimize, or if it did not help you'll need to contact your host and show them the PDF file you attached on this ticket. They can run the query and see why it's so slow that it gets interrupted by the server. Maybe the database needs repairing that's beyond what a non-privileged database user can do i.e. what we did with Admin Tools. A more thorough database repair requires root privileges on the server, something that only your host has.