If you're playing in Chrome the game pauses if you switch to a different tab (technical limitation with WebGL). Try opening the game in a seperate window, then it should continue to make progress while you're off doing other things.
The enemy AI doesn't really do anything. Some of my games they just sit at their starting position. Sometimes they'll move a unit or two over one hex-tile. But other than that I think it's a great game.
Buy all expansions, get butt-tons of cash, rip everything down and start over. That's what I did at star three. It is annoying how everybody is fine but as soon as I upgrade my reputation everybody starts complaining. Oh well, nice game.
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If you're playing in Chrome the game pauses if you switch to a different tab (technical limitation with WebGL). Try opening the game in a seperate window, then it should continue to make progress while you're off doing other things.