Moderators have thankless tasks including intervening in existing conflicts, or also enforcing rules users were not aware of. Of course, users are unpleasantly surprised at such intrusions, and not all of them react gracefully. Some of them start crying about moderator nazis and whatnot, or deleting their posts because somebody (a moderator or another user) said something negative. Of course, this angers me personally.
But our public site is there for everybody, and I believe that people who have a hard time psychologically coping with (real or imagined) rejection have as much right to use it as everybody else. Besides, I want to be a member of an open and kind community, and reacting aggressively or even just firmly blocking an angry or hurt user goes against these beliefs. And then there is the matter of us being a small community, so it is hard for us to lose users.
I do my best to be patient, but at some point it becomes too ridiculous. I had a case where me and a fellow moderator spent three days frequently communicating with a user over three different channels trying to convince him that two people posting comments doubting the veracity of a minor detail in their post doesn't mean that they are unwanted on the site. In retrospect, this was probably too much effort without especially valuable return.
What are good criteria to decide how far to go humoring a user who is acting up? Especially if he isn't involving other users in the drama, it is hard to draw a line and say that rejecting him and stop giving support has just become acceptable. I don't think that my own feelings are a good guide, because if I stopped cooperating at the first offensive reaction by the user, I'd be no better than them. So, what signs can I use to determine when the user is demanding too much?