Windows tip: Weblog gHacks details how to customize your system tray to selectively show and hide system tray apps
Right-click the start menu button and select Properties. Uncheck Hide Inactive Icons to display all icons. You could alternatively click on customize and select items that you always want to see.
If you prefer the behaviour as is, this isn't for you, but if you get irritated by the often-flaky behavior of that little arrow, this might be just the tweak you've been looking for.