Logic would like rather than the icon remains in the bar of menus while being grayed.

To start again Remote Buddy, it would be enough to click on the icon and to select the adequate function. 

thanks for your feedback.

This is not a bug, though, but rather the way menu items work under 
OS X. They can only be added from a running application. So, if 
Remote Buddy does not run, it also can't have the menu item in the menu.

The possibility would exist, to either

a) launch a helper application in the background, which would need to 
communicate via IPC with Remote Buddy and eat additional system 
resources

b) create an officially undocumented bundle for the system, save some 
resources, but still have additional IPC overhead and a good chance 
that the whole construct breaks or behaves unexpected due to the 
undocumented and unsupported nature of this undertaking.

So I think the way it is now is by far the best solution. If you want 
to temporarily activate or deactivate Remote Buddy, you can find 
respective items in the Remote Buddy menu item in the titlebar.

Best regards, 
Felix