Have you tried contacting MS support about getting it exchanged/replaced? How about the place you bought it? I've had a few wireless mice, and their batteries have all lasted longer than a month, but only one has lasted as long as 10 months. I have a MS
Natural Wireless Laser 6000 that they last 6 months, almost to the day. But the batteries in my Logitech V470 Bluetooth Notebook mouse last about 4 months, and it's turned off more than on.
I think you have a defective mouse, but I'm sure neither your merchant nor Microsoft would take my word for it :-)