Bluetooth hardware, which uses a complex, two-way, encrypted radio wave protocol, draws a lot more power than f.ex. classic and much simpler infrared based remotes that don't have to deal with any of this complexity.

Tip: take a look at the "How to maximize battery life" section for the Sony PS3 BD Remote Control: 
http://www.iospirit.com/products/remotebuddy/hardware/#sonyps3bdremote

Best regards, 
Felix Schwarz