avatars plugin causing randomly disappearing avatars

I'm having an odd problem that has resisted all my attempts to diagnose so far. We're using the Avatars plugin for a mulitsite install for American University. It's using Wordpress 3.1 with the 3.5.4 version of the plugin. Plugin is installed in /wp-content/plugins/, old version is not in mu-plugins, and there's no htaccess rule left behind.

The problem is that the author avatars randomly appear and disappear while the page loads. When the load is complete, random avatars are missing. A refresh will bring in some avatars and remove others.

You can see it yourself here:

http://blogs.american.edu/

Hit refresh a few times to see it. Any ideas?