You might consider something more mundane: hit by a comet or asteroid or fried by a solar flare. Or, more prosaically, there is no gate: the original colony ships were sufficiently fast that time dilation became significant; the various worlds of Firefly are sufficiently close that time dilation is not significant anyway.
As for Earth, I'll note that a really big player is missing from the intro: India. Maybe India decided to stay and take over the world? Maybe they had secret stores of resources and encouraged everyone else to leave?