Wireless mice use more power than keyboards - nothing you can do about it, except get a corded mouse or a mouse with a docking station. Both drain power even when the computer is off - firstly they don't know the computer is off, and secondly you might have it set for keyboard power on, or be on standby, or something.
Easiest thing for you would be to get a set of rechargables and a fast charger. I bought a MX700 to go with my cordless elite. Now I'm going to ge the MX desktop, so I've only got one base station, and so the keyboard will be in UK layout rather than US layout (I've come back home to England since I won an elite). The differences are only tiny, but really annoying. Either I can have it set to US, and have to use character map or something to get a £, or I set it to uk, and lose the \ key cos its not in the same place. ah heck.