I think the ZipArchive class is actually defined in our plugin, so I'm wondering if the plugin files were affected by the issues you had with your site.
Try this - download (from here) a new copy of the plugin and then log into the site over FTP to extract and replace the plugin files. That should replace any files that might be missing.
Let me know if that works. If it doesn't - are you able to enable support and send me a request with additional information through there?
Thanks,
Kat