Yes, they seem to gradually change color on their own. I have never died, yet my crystal has begun to show signs of changing as well.

[Jade takes out his own crystal. It's still red, but there's the faintest hint of violet in the center.]

The woman in the dream claimed our crystals contain time. When we are mortally wounded, we are restored to our anterior state -- in a way, our bodies go back in time. Perhaps the color change is directly related to the passage of time, then? It could explain why it progresses slowly in normal circumstances, but speeds up dramatically when the crystal is forced to alter our temporal state to such an extent.

[It's all speculation at this point, but it's a thought.]