How do I stop aluminium wireless keyboard from waking computer from sleep?

Question

Hi
My aluminium wireless keyboard wakes my computer from sleep, at random occasions. Sometimes after five minutes, other times up to four hours. Sometimes not at all. My iMac wakes up (annoyingly during the night, waking me up as well) and screen says "Connection Lost", showing the greyed out keyboard-logo. It's not lying either—keyboard doesn't work, for about 30 sec until the stupid thing finds it again and all is back to normal.
*What can I do to stop this irrational behavior?*
Could this be a bluetooth hardware-malfunction?
(Background: My iMac has been acting this way, as far as I can recall, throughout all of the 10.6.X-upgrades—from time to time. Reason I am posting this now is that I haven't had this problem for a couple of months now, but it came back out of nowhere the other night, about a week ago. And I haven't been doing anything out of the ordinary, that I haven't done at least a couple of times during this period where it all worked fine.)
Additional information: I don't know if this has anything to do with the problem at hand, but when using the bluetooth for something other than just keyboard+mouse, say syncing my Nokia phone, the mouse always goes haywire and acts all laggy, trickling across the screen as I try to move it.

Answer 1

Yes, that sounded indeed like a daft question, but as it seems changing the batteries did actually solve the puzzle. I am baffled by this, as the batteries claimed to be at 40% and shouldn't need to be changed. But I changed them after reading your reply, and the problem stopped. Now, one week and a couple of days later, the problem still has not reoccurred.
For one reason or another, once batteries drop under a certain level of power, the keyboard connection will start acting up. I feel a bit silly, should have checked that bit myself before posting my question, but I'm glad this solved my problem. Thank you ajduguid.