I'm having the same issues reported in a thread about Twitter Tools 1.5, but I didn't see a fix, and since this is a new version, I thought it deserved a new thread.
Am using Twitter Tools 1.6, with WP 2.7.1 and now 2.8 (but the problems started before 2.8).
Twitter Tools stopped working for me on June 1st. (My weekly digest posted on 5/31 but a post I made on 6/1 didn't tweet.) Since then, none of my tweets have appeared in the widget, and my posts are not creating tweets.
I just changed my password in case that was the issue. When I try to test my login in Twitter Tools admin, I get either "Sorry, login failed. Error message from Twitter: Rate limit exceeded. Clients may not make more than 100 requests per hour." or "Sorry, login failed. Error message from Twitter: This method requires authentication."
My poor little blog (www.megat0n.com) wouldn't have any content without Twitter Tools, so I'm anxious to hear any suggestions about how to fix it.