I have the same problem. It seems the plugin keeps using the cached tweet, even if the API limit has not been reached. I then disable caching using the Tweet Blender configuration (which says it will delete all cached tweets). However, it will not delete the cached tweets and it appears it is still displaying tweets from its cache. I then manually delete the cache from the Tweet Blender "Status" tab. Now (after disabling the cache and manually deleting the cache), it shows the latest tweet.
The above is not a workaround, though. I'd love for the caching to work as documented and this plugin would be great.
I am using Tweet Blender 3.3.15 with WordPress 3.4.2.