This situation is most likely to arise when working on larger sites and/or a page with a lot of widgets. It occurs at random for no apparent reason.
When a widget is refreshing or updating the content, a small green dot with a down arrow will appear briefly in the top right corner.
If any - or all - the widgets on a page show this arrow and they don't disappear, it means that the refresh is stuck.
This problem can also arise when a new widget is dragged onto the page or an an existing one is modified. A new widget may appear as a grey rectangle with the refresh button showing continuously.
An existing widget may remain the same with the refresh button showing even after making changes to the widget settings.
When this happens, save (command S), quit EverWeb (command Q) and then relaunch the app.
Now force the widget(s) to refresh by dragging it slightly wider with one of the drag handles and then returning it to its original state by doing command Z. The widget will then update itself.