So, the Lore never tells us, but I think I know what's chasing the Vasari.
For those of you who bought Sins at the store, take a look at the back of the box. It says at the top:
"Assume ultimate control over one of three galactic powers: an ancient alien civilization running from a terror of their own creation, a loose coalition of traders forced to annex their own people or an exiled empire of powerful psionics bent on revenge. Will you lead them to salvation or condemn them to extinction? The choice is yours..."
Notice: "an ancient alien civilization running from a terror of their own creation"
The ancient alien civilization is of course the Vasari. A terror of their own creation? Well, thinking about what the Vasari excel at; phase space and nanorobotics. I think that most likely what they are running from is a nanobot problem. Search "Gray Goo" on Wikipedia and you'll get a bit of an idea of why it would be so terrifying.
What do you guys think?