The specific issues vary, but they all have one thing in common- drama. One person creates it, everyone else has to deal with it. There's a useful article on this topic at the the ADF website, called “weeding the garden.” It might not be very nice to think of certain people as being like weeds, but the analogy is a valid one. When a single member of the group is ruining the experience for everyone else, that person has to go.
Of course, you don't want to jump to that conclusion, and nor should you. But once you start losing other members because of the actions of a single person, you have to ask yourself- is it more important for us to keep this one person at the expense of everyone else, or do we need to lose this one person for the sake of everyone else?
According to the article, the biggest mistake you can make is to explain yourself to the person in question, because they will use that as an opportunity to debate the issue with you in detail. Instead, you should just let them know that they aren't a good fit with the group, you wish them well, but that's that.