Looks like I have a similar problem, which started with updating 3.10 to 3.1.1 (and now to 3.1.2). Since then tweet-blender doesn't update tweets manually nor automatically. I reduced from 3 sources (which I'd need) to only one and tested in at least 3 different recent browsers (FF, IE, Opera).
Site is live at http://news.prva.at, server is Apache 2.2.3, PHP 5.2.x, MySQL 5.0.x
Modifications to tweet-blender files I made:
tweets.css: inserted a line-height at line 83
tweet-blender.php: added a few words in the Description (line 5)
widget.php: translated "more tweets" to German (in lines 64 and 67)
And, yes, I was very careful with those changes, checked a couple of times ;-)
Your help is very much appreciated.