Remote Buddy would need to be able to detect the button press to 
react to it and to establish a connection. But then, without a 
connection, a button press can't be detected.

The comparably high power consumption is simply a limitation of the 
Bluetooth technology. However, you keep your costs low and the 
environment clean(er) using rechargables. I've bought a bunch of 
those when I started adding support for the BT based remotes.

Best regards, 
Felix