Ouch, I think i'd rather use regular alkaline then and change them every 6 months.
I am quite sure that even alkaline batteries won't hold six months if rechargable batteries are emptied within six days. I've got a Logitech Ex-100 desktop and still use my rather old 800mAh rechargables and they last at least two or three weeks. Actually I cannot tell how long they really last because I don't remember when I needed to recharge last time.
The keyboard is even better. It uses the smaller AAA-sized batteries and they last for at least six months with one charge.
A cheap mouse does not necessarily mean that it costs less money if you take battery usage into account.