I am having the same problem with a website I have built for a client.
http://www.jackwrightdesign.co.uk/index.php
The Twitter feed will intermittently stop working. I am using the exact same plugin I use for my own website and the Twitter feed there works fine.
http://www.eggywebdesign.com/
This suggest to me that the problem may be caused by either:
My clients hosting service (Zeus hosting, which has proven to be problematic already with permalinks)
or the small number of followers my client has for his Twitter profile.
Do either of these suggestions seem feasible?
This tutorial for “Twitter for WordPress” helped me.
http://rick.jinlabs.com/code/twitter/