The support of large files actually depends on the host. Akeeba Backup chops each file to upload in 5Mb parts and starts pushing them to Amazon, one at a time. At the end of the process it asks Amazon to glue them together into a single file. If the parts can't be transferred fast enough, the connection used to upload them times out and you get the error you mentioned.
Unfortunately, there's no workaround to that issue other than using a host with more outbound bandwidth available, or at least trying to backup your site in off-peak hours. A good way to determine off-peak hours is using the pageviews view of Google Analytics and clicking the clock icon. You'll notice which time of the day (expressed in the California time zone) is the least busy of the day for your site and -most likely- a good candidate for running a backup on.
Nicholas K. Dionysopoulos
Lead Developer and Director
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