I noticed this was never answered and sort of overdue but figured I'd help you out since I've worked a little bit with my theme in terms of integrating Disqus and was looking for this solution but didn't come across this so I setup my own cron job. It requires access and a bit of knowledge setting up a cron job in Cpanel.
1. Locate this file /scripts/export-comments.php in your Disqus plugin folder.
2. Copy complete path to that file, should be /wp-content/plugins/disqus-comment-system/scripts/export-comments.php if you have default plugin installation.
3. Goto your site's cpanel and open the Cron Jobs link
3.a: In the e-mail field put your email
3.b: Set how you want to run your cron job, every hour? every day? In cpanel you can select the dropdown selection of what you want to do , I chose once an hour which is 0 * * * *.
4. In the command section put this php -q exportscriptfileurl
Example: php -q /wp-content/plugins/disqus-comment-system/scripts/export-comments.php
no output will be generated, except what your script explicitly sends to stdout - which is good.
The -q flag will keep php quiet and is recommended for running scripts via cron.
Now you should be exporting comments automatically assumming you got it setup right. If you didnt let me know and I can help troubleshooting.