Forgive me as I'm new to DW CS4, but I may have a solution. I encountered the css copy problem as well, but I turned off (unchecked) "Enable Related Files" (Edit -> Preferences -> General -> Document Options -> Enable Related Files). I had to restart Dreamweaver, but this seems to have fixed the bug.
I've never used the "Enable Related Files" feature, so it's not a big deal to me - much less of a big deal than not being able to copy and paste. At least it seems to be a stable work around to the "css copy paste" problem.
Hope it helps! Let me know if this resolves the issue for anyone else.
-- Trevor
Vista Home Premium 64
DW CS4 Version 10.0 Build 4117