The ring changed its size to make itself appear more desirable to whoever held it. Isildur said it seemed to change shape in his hand, and he took it for himself. A dragon would only keep the ring because it was gold and they keep gold. They don't use what they keep, they just keep it to have it.
So a person would say, "Oh, here's a pretty little ring, and it's just my size!", and then keep it.
But a dragon would say, "Oh, here's a pretty hula-hoop. It will go good with my collection.", and toss it onto his mountain of treasure and forget about it.
The dragon would not use the ring, so the ring would have little reason to change its size to be desirable to the dragon.