Hello,
I think there is some problem with Itemid in the URL for new articles. Probably when you create a new article, the wrong Itemid is stored in its URL (probably the Itemid of the menu item used to create the article), so Joomla then according to this Itemid thinks, that it should be accessible only for the registered users (or even editors maybe). After deleting the URL in database, it gets recreated from the link present on homepage or other publicly accessible menu item, and stores the correct Itemid to the link.
Unfortunately, this behaviour depends on your menu structure. As a general solution, you can try one of these:
1. Go to Manage Extensions, open the Content parameters and on the Common tab set "Ignore multiple sources" option to "No".
or:
2. Go to JoomSEF configuration and on the Advanced tab set both the "Exclude source info" and "Reappend source info" options to "Yes".
Best regards,
ARTIO Support Team