Benjamin,
I was having the same issues as you. The comments form would disappear after changing to registered users only. Here is what I did, although my users are registered, they are under Joomla registration as registered. You need to go into K2, click on each user and assign them to the User Group "Registered". Also go to the User Groups tab and select Registered and make sure you have enabled comments for this group.
I had to go back and manually do this for about 500 users, very frustrating. There is an option in the "K2" registration form to have them automatically put into a user group, IF you are using the K2 registration this will work for future registered users. I am using JomSocial registration, so until K2 integrates user profiles from JomSocial I am going to have to manually do this for every user......