I'm kind of on the fence, truthfully. Often, when a character first refers to another by a new nickname, it won't be capitalized at first, as it's not clear in the story yet that it's anything other than a one-time occurrence and thus not worthy of being treated as a real nickname.
However, should the character continue to use this name (or have the name used on them), I'll usually start capitalizing it.
In my current story, the name "little winter girl," first applied in passing to a girl with white hair, seems to have caught on so now when various characters call her this it's "Little Winter Girl." However, when they're using it more like a descriptive term rather than a nickname, usually when not addressing her directly ("that little winter girl" as opposed to "Hello, Little Winter Girl"), I won't capitalize it.
So I guess you could say I'm rather inconsistent, and that kind of bugs me. :/
If it's a true nickname though--as in a real name that's well established ("Charm" in place of "Charmian") and/or clearly treated, from the start, as a nickname (one character starts calling another "Little Sister," for example)--then I'll always capitalize it.
I agree in that, usually, terms used in passing, like "honey," "babe," "sweetie," etc., shouldn't be capitalized. Unless one character makes it a point to always refer to another character by such a name.