We’ve made some research about the problem and here is the situation:
The current code (the one that is not working) is a part from the old deprecated Twitter API (version lower than 1).
We will now submit a patch based on Twitter API v1 – you can check this topic for more information.
Unfortunately the solution is only temporary, because sometime in March 2013, Twitter will drop the support for v1 of the API as well.
The next version of the API will require authorization, for everybody who wants to get information from twitter (tweets, msgs etc.), so we will need to rework the twitter widget a bit. The new widget will be available with the next Shoppica update.