Hi Sam,
Has anything changed in your setup around the time the excessive battery drain started? The Bluetooth communication between the mouse and your MacBook is susceptible to interference and will thus have to boost the power output in order to maintain contact.
Although I didn't find any information specific to your mouse, I did run across a couple of guys having power drain issues with a different Logitech mouse. The first guy had a cordless phone too close to his setup.
[quote]My Logitech K800 wireless keyboard ran a long time between charges until I replaced the landline phone on my desk with a Panasonic phone with DECT 6.0 Plus Technology. This caused the logitech keyboard battery to run down in a few hours. I put my old ATT phone back and the Logitech keyboard works fine again.[/quote]
Another user apparently had a problem with dust in his mouse.
[quote]My Logitech mouse had slowly started eating batteries more quickly until I was replacing them every few days. I just blew some canned air into it really well and now it's working like a champ and not sucking my batteries dry![/quote]
So look for any wireless devices that could be interfering with your mouse, and give it a good cleaning and let us know what happens.