Waking the machine on a connection attempt from a paired Bluetooth device is a low-level feature of the OS X Bluetooth stack that applications have no involvement and no control over. It also has nothing to do with App Nap (in fact, being a low-level feature of the OS X BT stack, waking the machine with a paired Bluetooth device will even work if Remote Buddy is not running or even was uninstalled completely).

Unfortunately, if this feature of the OS X Bluetooth stack doesn’t work correctly on your machine, I pretty much have no way of debugging or addressing this issue, as it’s not happening inside my code.

Purely speculative, but: 
You may try to remove the remote from Remote Buddy Prefs > Hardware > Bluetooth Receiver (and only there) and perform pairing with the Setup Wizard again, in the hope that the OS X Bluetooth stack refreshes the device data it stores inside the Bluetooth chip, so that a connection attempt from it wakes your machine the next time.

For what it’s worth, waking my test Macs (including a Mac Mini) via a Sony BD Remote under Mavericks works without issues.

I’m sorry that I can’t really provide any help beyond this.

Best regards, 
Felix Schwarz