You know, Sarge, this has to be a hardware problem allied to some Logitech mice. There's a user here in Cebu who has an HP/Compaq (widescreen) laptop running Windows 7 64-bit and a USB (HP) external mouse. He has absolutely none of the problems you and Worick are encountering. My wife uses a Dell Studio (1737) laptop, under Windows 7 64-bit, and it has a 3+ year old Logitech wireless mouse and that also works flawlessly with Circle Dock.
That said, there is one last thing we can try. Up to now, the global handler has been raising events within Circle Dock whenever a mouse activity is detected - such as you moving the mouse, mouse button down, mouse button up etc. I've made a minor modification such that when the button used to toggle visibility is released, a message is sent to Circle Dock's main message handler (its WndProc) and this in turn toggles the visibility. Different mechanism, same result.
I've kept in all the mouse event handlers, however, but now these simply report the mouse's status. I've also retained "keep alive" although you should not need that now. (Incidentally, the "keep alive" function monitors two aspects. It is triggered after 30 seconds of mouse and keyboard inactivity; it is also triggered once every 50 keystrokes unless there is mouse activity during those keystrokes.)
If this version still misbehaves for you, then I'm at a loss as what to do next.
Oh yes, I almost forgot: there are two circumstances where Circle Dock needs to restart itself following configuration changes made in the main settings dialog. The first is fairly obvious - change of UI language. The second is where the default Z-Order is changed. If you modify either of those settings, Circle Dock will automatically restart itself when you close the settings dialog (it's no longer necessary to press the big button on the languages page - the button itself is being removed).