Been thinking about this for a bit, and I noticed a bit of a pattern.

It seems like 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 onto something here? Perhaps... But it could also be discussed.