First let's make sure it's not something simple. Download the latest version of our software, extract the ZIP file locally and upload the extracted akeebabackupwp folder into your site's wp-contents/plugins, overwriting existing files. This will make sure we're not having some code file which hasn't been updated causing the problem.
If despite doing that and using an imported known good profile we can discount the possibility that it's something with Akeeba Backup. You'll have to ask your host to take a look. Most likely they are using a cache or proxy in front of your site's outbound requests. They need to disable it for DreamHost's API endpoint (objects-us-east-1.dream.io per their documentation