I have had to do this three times over the years. It is not an easy thing to do and is the absolute last resort after all else has failed.
I feel that as long as a student is making SOME progress and the general "learning curve" is going up over the long term I'll work with them and do whatever it takes for them to make a breakthrough. I have seen some extremely unlikely students work their way through problems and become competent aikidoka. There have been tears flowing (from everyone) in my dojo on many occasions as these folks make demonstrations for advancement.
However, we must understand that some people just don't have the tools. When the time comes to tell someone that they should try some other activity the only way it can be done is privately, gently, and by giving them the feeling that it isn't "the end of the world."
As an aside...many of us have been told that we can be or do whatever we want as long as we want it enough and work hard enough for it. I think that's the sure way to know whether you can achieve something or not, but we can't all have the tools necessary to be an astro-physicist or a world class concert pianist for two examples. We have to find and know our limits. If not we are programming our own unhappiness.