The Cloak of the Dark Moon seems to prevent the Ring of Regeneration from working. I keep one around for topping people off between fights to conserve potions, and noticed Dorn wasn't healing up at all. I removed all of his gear but the ring; he started regenerating as normal. I then added gear back one piece at a time, and confirmed it was the cloak. Note that he still gets the 'Regenerating' portrait icon. This occurs regardless of which item is equipped first.
This doesn't seem to affect all regeneration, as the Ring of Gaxx still works with the Cloak of the Dark Moon equipped. Zipped save game attached. Notice that he isn't regenerating; remove the cloak and you'll see the regeneration kick in. He doesn't have any other statuses (statii??) applied, other than his innate immunity to fear and level drain. You can also equip the Ring of Gaxx he has in inventory to see that it isn't affected by the cloak.
Note: I tested this on other characters, and it seems to have the same effect. However, sometimes the regen kicks in even with the cloak on, and I haven't figured out what the difference might be.