There have been a few justices in the past that have "gone off their rockers" in the last few years of their careers, but from what I understand, unless they retire, they couldn't be replaced. But what if the Justice was in, say, a coma, and was therefore physically unable to work and unable to retire - is there anything that can be done to choose their successor, or would the only options be to wait for them to wake from the coma or pass away?
Federal judges and the Supreme Court justices hold their office during "good behavior". You could argue that being in a coma (or some other issue) is not "good behavior" and initiate impeachment and removal proceedings. This is untested though and may be considered a nuclear option.