I have a mini-theory that his healing powers work depending on how much he cares about the individual being healed. Remember that it was after he failed to heal a crack in a geode that he became dissuaded from using the power (Greg tricking him into thinking it didn't work weakened it, but didn't completely turn him off). Of course he wouldn't have many feelings for a (non-sentient) rock, but the others that he's healed he has cared about in some way or another.
Connie: Best friend and possible romantic interest
Lapis: Beach Summer Fun Buddy
Greg: His dad that he's always loved
So maybe I'm on to something here? Perhaps... But it could also be discussed.