Official Twitter widget randomly not pulling feeds across multiple sites

I have used the official Twitter widget to pull Twitter feeds and searches into a number of WordPress sites but over the past few days it has started to fail intermittently.

Sometimes the feed is there, as normal, but other times it is just a big space apart from the “Tweets by @” at the top.

This is happening for me on a variety of sites using entirely different templates and across browsers.

Has anyone else noticed this? Can anyone suggest a solution?

Many thanks.