There seems to be a problem when your remote tries to build the connection to the OS X Bluetooth stack - or when the OS X Bluetooth stack tells the remote that it'll close the connection. Remote Buddy only enters the picture later, after that connection has already been established, so this unfortunately doesn't look like an issue Remote Buddy has any influence on - or any chance to fix.

Are you using a Bluetooth USB stick or a Hackintosh by any chance?

Did you try to with fresh/fully charged batteries?

Best regards, 
Felix Schwarz