Elderling Creations Theory (Spoilers through all the books and Dragon Haven)

[maulkin]

One possibility is that the memory stone of the stone dragons is "full". It has received enough memory to animate it and now resists acquiring any more (this would merely disrupt its identity). Because the stone is no longer passively acquiring memories, it is no longer dangerous to living organisms and so they are no longer repelled by it. An argument against this is that the stone dragons do still seem to steal memories when they are active, to the extent that people can be forged merely by being overflown by a stone dragon.

An alternative possibility is that, by becoming dormant, the stone dragons inactivate the power of the memory stone to soak up memories/life force. It is possible that, if the dragons did not shut down this property of the stone, their sleep would interrupted frequently as they accidentally absorbed memories and life force from wandering animals and questing plants. This seems to make sense, given that the dragons can be awakened by intentionally splashing them with blood, effectively forcing them to absorb life force.