Sometimes it happens that Twitter feed isn't shown even with correct Twitter username entered. In such case most likely Twitter limit is exceeded.
The issue can be solved if you register new twitter API keys for your domain. The keys are added to the appropriate fields in Theme Settings - General - Custom Codes:
To generate new keys please proceed to
https://dev.twitter.com/ and log in using your Twitter login data. Open My Applications tab
click "Create an app" and fill in the form: