I did as you suggested. I also noticed that this licence was not listed in the “Manage License” section of my accound page (https://ajdg.solutions/my-account/manage-license/). After reactivate license, it is now ok and I can see it. I test the automatic update by temporary modify the version number in file adrotate-pro.php and wordpress detect the update.
So the issue can be closed 🙂
Thanks again for your help and for your great plugin.