This was driving me nuts, as it's the best plugin I could find for the way I wanted it to look. So I decided to fix it myself.
I've made a number of changes to my plugin for display purposes so I can't give you precise line numbers. Basically look for the following line:
$options[CURLOPT_URL] = 'http://twitter.com/statuses/followers/'.$instance['twitterfans_username'].'.xml';
(in mine it's line 89)
Comment it out (always comment before committing!) and add the following line in it's place:
$options[CURLOPT_URL] = 'http://api.twitter.com/1/statuses/followers/ids.xml?'.$instance['twitterfans_username'].'=twitterapi';
I also uncommented the line :
$twitter_fans = get_option('twitter_fans');
Not sure if it was something someone else here in my office commented out, or the original developer, but I put it back in anyway. Haven't had time to assess it's true functionality.
Change the number of fans in your widget (to force a cache reload of the fans) and refresh the page. Should work fine.