(Assumes that either they draining resources from smaller asteroids rather than terrestrial planets, or that they eat planets so thoroughly that basically all of the planetary mass is converted to goo, with no atmosphere remaining.)
The Jorō spider is known for being beautiful, for being aggressively invasive, and for flying. When introduced to a new area, they set up their meticulously-crafted webs, decimate the local insect population, and then breed the next generation. Those hatchlings use their silk not for webs, but for "parachutes". They extend a strand into the air where the wind can catch it, and catch it it does, lofting the hatchling into the air. It can't control its direction, but when it touches down again, it will try its best to build a web at the new location, continuing the outward invasion.
The Jorō goo behaves similarly. After devouring a planet, an insanely large number of bots rest in their own gravity well, exposed to the harsh radiation of the sun. Those who feel the hardest of the hard radiation extend a small sail into the solar wind. At first, nothing happens; resources to build a big enough sail to escape a gravity well just aren't to be found. But eventually, within a few decades, the ejecta from a solar flare washes over the planet. The magnetic fields of the CME charge the sail, and the high-energy protons in the ejecta slam into it. For most of the trillions upon trillions of goo bots, nothing happens. For a small percentage, the radiation destroys them, or nearly so; flips bits of memory and corrupts their software and behavior. And for a tiny bit of a tiny bit, enough momentum hits at the right angle to fling the bot out of the gravity well and into space.
With trillions of trillions of bots on a planet, its hard to imagine that only hundreds or thousands may escape the well. But once they do, they travel through space for a long, long time. Some are accelerated by the solar magnetic fields into interstellar space; some end up in an orbit that goes no where. But if even one should land on another planet that can be mined...
The invasion will continue.