Q: What happens if you use the OS X Bluetooth-Menu (in the titlebar of OS 
X) to disconnect the BD Remote?

A: Remote Buddy sais: "BD Remote Control Disconnected", when i press any button on BD remote again, everything works great (of course with little lag).

Q: Can you see anything Bluteooth-related in Console.app's log (in "All 
messages" view)?

A: no

Q:Please also let me know, what your settings in Remote Buddy > 
Preferences > Hardware > Bluetooth Receiver are.

A:http://www.grabup.com/uploads/c2bf4d2a0e9de464be651c88e37cb07d.png?direct

 
My investigation: 
When RB disconnect BD remote and i press any button, in Bluetooth system-menu (OSX) is BD activeted, but not in RB. 
Some screenshots: 
After RB's Sawing Power and pressed button on remote to wake up: 
http://www.grabup.com/uploads/9ddf9ce376333c47f264fbd2bb0daec6.png?direct 
http://www.grabup.com/uploads/e26339f30979c1a747ca109af874c03c.png?direct

when i click to "Bluetooth Receiver" to "red icon" and again to "green icon", it works immediately without message "press any button..."