If you look in the comments on the Twitter Widget Pro page, you’ll see that there are more than a few people that had this issue (and I think they all solved it).
About 90% of the time this is because your particular account is reaching it’s API call limit. Twitter limits the number of calls that you can make in an hour. If you use something like tweetdeck, twhirl, Seesmic Desktop, etc, then each request that those make is counting toward your total. With the older versions of Twitter Widget Pro, if you didn’t have some sort of caching solution set up, each page load was another request to Twitter. It’s very easy to exceed the 100 requests per hour limit. The new (1.3+) versions only check twitter if it has been at least 5 minutes since the last time if checked. That means no more than 12 requests per hour. Still, if you’re using other systems with that username, you may have exceeded your limit.
Additionally, if you’re on hosting that has a poor connection to Twitter (or slow servers), then you may need to increase the number of seconds to wait for a response from Twitter (default 2). This is in the widget settings. Just don’t set it too high because if twitter is down it WILL wait that long for a response before continuing.
There are also some people that have had to ask their hosting company to allow the requests: “Although my hosting company allows access to cURL, all outgoing requests are blocked by firewall by default; a separate/manual support request is necessary to allow outgoing requests to any outside server. I’m guessing the other folks who are running into this issue have similar hosting setups.”