In a quick ruling today on a motion to quash, the justices refused to throw out the case, saying it will get a full hearing later this year.
The case pits the family of Hassan Rasouli against his doctors over the question of when doctors can withdraw life support.
Rasouli had been diagnosed as being in a persistent vegetative state and his doctors wanted to pull the plug over the family's objections.
The doctors went to court to clarify who may make such a decision and when.
Recently, Rasouli has shown some signs of awareness and the family sought to quash the appeal as moot, but the justices rejected that.