I like this question and I think that lil could have some valuable insight to throw in. I will quote from a PM she and I were having a while ago, about a not dissimilar subject. We were talking about someone who is no longer my friend.

I was having a conversation with a possible new friend the other day and I mentioned my friend theory: There are friends who are your friends and friends who are part of your caseload.

He interpreted this quite wisely by saying to me this: "By 'part of your caseload' you mean that you have an inherited sense of obligation to this friend."

Is that the case with this woman - perhaps because of your previous relationship and other shared events -- you have inherited a sense of obligation that you are now trying to shake?

I defined "friends who are my caseload" as friends who generally take more from us than they give - that we leave an encounter with them feeling depleted rather than enriched - but we continue it, as Pierre said, because of an inherited sense of obligation. Nonetheless, you do not miss them when you don't see them, and you do not initiate contact with them.