I am running into the same issue. I am running WordPress 2.8.4.
It is not a chron issue - working properly for other plugins.
The tweets are being captured by the database - it is not the Twitter API.
Have tried resetting the digest, reset tweet checking, updating the tweets, etc. Also tried deactivating the Thesis Theme, eliminating all plugins except Twitter Tools, reinstalled Twitter Tools.
All indications are that there is some form of bug within Twitter Tools impacting the Weekly Digest functionality.
Hope Alex can help...