I don't have too much specific to offer, but I see similar kinds of lag in my games, after a while. Not as frequent or severe as you describe. In general, make sure your graphics drivers are all up to date. Also make sure you've gone into online mode recently to get the most recent updates for the game. You can try playing in online mode full time, or with DX9, but those shouldn't affect much. You can also tweak some of the graphics settings downward without much loss of visuals but decent gain in performance. In particular, I find the mid settings for fog of war and water animations give big gains without looking bad. Windows and Civ 5 are both known for their memory leaks, so that's likely what you're running up against. The more units and terrain features you're animating, and the higher performance levels you're running them in, the faster the leaks will accumulate to the point of unplayability.
Hope that helps some. You can try exploring the
tech support forum for additional help.