Twitter has retired version 1 of their API causing some widgets to stop working.
Some users may be having problems with their twitter widgets and RSS feeds. This is because Twitter has retired their API that supports the older widgets and RSS feeds.
For users replacing their existing widgets twitter recommends embedded time lines (https://dev.twitter.com/docs/embedded-timelines)
For users replacing the RSS feed widget that agregates a bunch of feeds it is suggested that you create a list in twitter and then use the embedded time lines widget to embed the time line into an HTML widget.
You can create your own twitter widgets for embedding here https://twitter.com/settings/widgets