I have a horrible video card and it runs smoothly , its not that

BD completely fails when I use Google Chrome, or Windows Explorer, but it works fine on the Safari Web Browser which I suggest you get, although it lags just a teensy bit..

flash is run from the client, thus it uses more RAM/processor power than just a normal webpage.

When i heard that it ran fine the first few minutes, i immediately thought of checking how much space the flash file is allowed to take.
To check/change, right click in BD, click "settings", then click on Local Storage. It will allow you to set how much space it can take up, and how mcuh it is currently taking. The more space you give it, the shorter the re-load times for the game (passing ticks, and refreshing game), but the slower the game will run as you play more. The smaller the local storage, the faster the game will run each time, but the indivual loadings will take longer.

And again, since it is client side, you'd want to check your task manager to make sure that your system resources aren't stretched too thin.