Aryanna and Renwold, your issue sounds like mine. Does the problem go away if you zoom in on your Demigod? Zoom and move around to a different part of the map? I've noticed this can help at times.
Also, does it happen in multiplayer?
Like I said, I think this happens when the AI calls get to be too much, it overloads the processing, and sucks the framerate down.
-HM
Zooming out doesn't make the problem go away. MP? I didn't even touch MP yet, because of all the issues I'm already having (getting the game to work properly). The only thing that helps is, like I said, put the /nosound option in. With the /nosound option I have absolutely no problem whatsoever (except that I don't hear any sound obviously, which is highly irritating). I run the whole match with 30-40 FPS and round and about 4-5 simspeed. Without /nosound, I start off with that, but some minutes in, the FPS drops to 2-3 and the simspeed to -1/-2.