Switching to K2.0+ did not fix it.
But an interesting development is that the itemid in the URL is now 150. 150 is assigned to the menu item "Kunena Search" in my main menu (not the kunena menu) which is currently a non-published sub-menu item.
If I publish this item, just to see what happens, the itemid within the URL in the uddeIM inbox for the link to a profile changes to 148. When I unpublish it, the itemid changes back to 150.
Since I last posted, the only thing I've changed on my site was to add a new menu, and then changed my mind and deleted that new menu. I have not adjusted my main menu, nor the Kunena menu.