To increase battery life for the Sony® BD Remote, you should turn on the power saving options Remote Buddy offers. You can find them at Remote Buddy Preferences > Hardware > Bluetooth Receiver.

These settings are recommended:

General

Search for paired remotes on startup: On.
Stop searching for paired remotes after max .. minutes: Off.
Display pairing instructions and status messages: Off. If you experience problems, you should turn this option back on to aid you in debugging the problem.

Energy saving

Automatically disconnect remotes after inactivity of more than .. minute(s): On, value of 1 minute.
Disconnect remotes when computer goes to sleep: On. The potential power saving with this option is huge. But as the warning says, this will not work with all computers: if you can't wake up your computer with your remote after turning this option on, please turn it off again.