Umbraco 13.8.1 and xStatic

We have an Umbraco application where we use xStatic to create static HTML files of all content which is then transferred via FTP from the CMS server to the public web server. The versions we have used so far are Umbraco 13.0.3 and xStatic 3.1.1. It has worked very well. Now we have tried upgrading to Umbraco 13.8.1 and xStatic 13.0.1 and then you have to press “Save and publish” twice for the new content to be included in the generated HTML pages.
I have also tested different variants of Umbraco version 14 with xStatic and it is the same problem there. Does anyone recognize the problem or have any idea what it could be?

When I test the latest version of Umbraco and the latest version of xStatic it seems to work.