Just updating an older Site Builder site which has published saved searches of Items. The Item search is published and displays. If we try to click through the list we get Permission Error you need Lists >> Items Permission. The Publish search is Disallow Drill Down = F. The same items appear through other pages in the website just not linkable from the Publish Saved Search.

Check the role on a registered website customer (system information. access tab). Edit the role, or create a new customised role (if it's just "customer center") and add the permission.

Using Customer Center role does not allow me to add permissions. I can edit the existing limited list of permissions but not add additional permissions. In the meantime. I trashed the previous searches, recreated and now it's workings. Let's see if the gremlin returns.