Simply put, over the course of the game the animation on the surface of stars gradually slows down and stops, and the texture takes on a pixelated look.
When watching a replay, within 30 minutes the animation appeared to move at about normal speed only when running on 8x, so it slowed down to about 1/8. Not sure if the animation itself is what's wrong, or if the pixelation of the star just makes it appear to vanish.
After several hours the surface of stars are static aside from the occasional colored pixel turning white, or white pixel becoming colored.
This is what it looks like at the start (One) and later (Two and Three):
One
Two
Three
View the first and second at maximum size and switch between them to get a feel for what's happening to the texture. The third shows the pixelated star closer than the second.
Browsing through people's screenshots on Xfire I see a lot of stars in a state that looks much like mine eventually get to, so it's probably a common problem.
Specs:
NVIDIA GeForce 8600M GT (Dual with SLi, 185.81 drivers currently & issue happens with others)
Intel Core 2 Duo T9300, 2.50 Ghz
3GB RAM
Vista 32-bit