Analysis tools added to the widget of a Web AppBuilder for ArcGIS application cannot be executed multiple times in a single session when the 'Save the result in user's account' option is disabled.
1. Reload the application and rerun the tool. Note that the results from when the tool was previously run will be lost.
2. Ensure the 'Allow to export results' option is enabled in the tool settings.
3. From the edit option of the application, enable the 'Save the result in user's account' option, and the tool runs as expected.