Ok, while I was debugging this in your site, I found that although the API calls to mailchimp are going successfully the ajax calls for sending the data are breaking in between.
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Which stops all the progress in between and no matter how much you wait it will not finish because it has been truncated by a background process.
Since all 5XX errors are recorded in server, we need to check the PHP error log in your server for further information on this. Alternatively, you can also give us FTP credentials and in case this is a live site, also mention the time during which we can debug your site for this.