It's 12 years later now, but yes i am having this problem with my new windows 10 laptop. The arrow keys either don't function at all, or they stop functioning after a few games in some flash games. Specifically 8-ball pool by miniclip. I had some issues with the arrow keys that were corrected by windows updates, but some problems persist at 8-ball pool by miniclip for some reason.
The arrow keys works for me in the final projector exe, I'm on Windows 10 (64-bit).
Unrelated: The "Control > Step Forward" and "Control > Step Back" keyboard shortcuts does not work in the projector however (Ctrl + left/right arrow key). I think that has been bugged for many years. Adobe never cared about fixing it. The control shortcuts for Play (Ctrl + Enter) or Rewind (Ctrl + R) works.
Given that the original post was from 2009, I'm going to lock this thread. The original poster doesn't want email updates on this topic, and I hate to spam them.
Flash Player is end-of-life on December 31, 2020. We're actively encouraging people to uninstall at this point through both public messaging and pop-up notifications. For convenience, I've included links to the uninstallers below:
Uninstall Flash Player - Windows:
Uninstall Flash Player - Mac:
To answer your question, it's really dependent on how the developers wrote the game. Depending on the OS and browser combination, the underlying key codes changed in the last couple years. That sometimes breaks assumptions made by the underlying game. You could experiment with different browsers and/or the standalone player, but again, you're probably better off just finding a game that isn't dependent on Flash Player at this point.