The combo I had was indeed Logitech, their Bluetooth Cordless Desktop. I've heard that the Bluetooth radio based devices suck more power, so that could have been the cause.

I now have a Logitech Wave corded keyboard (love it), and an MX Revolution cordless mouse. It consistently lasts 2 weeks, as I'm charging it every other weekend. The MX Revo was released before the Cordless Wave Desktop, so it may still be slightly more power hungry technology, but is already twice as good as my previous.

Pioneer PDP-5020FD, Marantz SR6011
Axiom M5HP, VP160HP, QS8
Sony PS4, surround backs
-Chris