I think I know what you mean. It's when you save a game, closes down Civ3 and when you later restarts and reloads that game, then the animations no longer plays (for instance a worker building a mine just plays default.flc while he actually is performing the build-action). This behaviour happens in my game too (modded game). I noticed it first on the user-made units, but it is possible that Firaxis-units are affected as well. It don't know why this happens, though.