Thanks for getting back to me.
The table in question is not a global table. There is one created for each site that the plugin is used on. The plugin adheres to the WP table prefix. In this case, the prefix is "bl0g_", therefor a site with an ID of 123 has a table named bl0g_123_client_info.
Is it possible that it's not working correctly because I'm using a custom table prefix? Or could there be any other reason this isn't working?
Oh snap... I just figured out the problem. It's an issue with the plugin. It has a column in it's table that defines the site ID. Probably under the assumption that all sites share a global table. Since the table is cloned to a new one, the blog site ID doesn't change.
This should be an easy fix in the plugin now that I know what's happening. Sorry to unnecessarily bug you. And thank you so much for your time.