Unfortunately, the latency (ping) with satellite internet is normally too high for any online action games. Turn games tend to be okay, but nearly any game that relies on quick movement will range from frustrating to downright unplayable. And, though I don't know for sure, as I don't have an Xbox, I'm wondering if the high latency itself is what's causing your system to be booted from their server.
As well, there's really not anything that can be done about the latency. About the lowest possible with geostationary satellite internet is around 550ms, but it averages between 600ms and 700ms, for most people.