Could be a dead logic board battery, the so-called "PRAM" battery. The battery preserves user settings when the computer is unplugged from the wall. Normally, even in the presence of a completely dead battery, settings should "stick" as long as you don't unplug the computer.
If you are trying to save energy by either unplugging the computer at night or turning it off at a power center or power strip, that's not a good practice with many computers. The internal battery should normally last 3-5 years as long as the computer is plugged into an active socket. If you cut all power to it, the battery life can plummet to months, and settings will not be remembered.
Fortunately the battery is cheap and user-serviceable. I buy mine here:
If you cannot order batteries for that firm, the link has the full specs of the battery: 1/2 AA 3.6V lithium.
Radio Shack ("Tandy" outside the US) carries the proper battery as part number 23-026 but will charge you 3 to 4 times the online cost.
Installation is easy--you access the battery through the same "door" on the bottom of the case through which you access the RAM. Apple instructions are here:
A quick check to comfirm the battery as the issue is:
- Restart the computer while holding the four- key combo command + option + p + r (may not work from a third-party keyboard)
- Keep holding those keys until you hear three startup chimes
- Set the birghtess to the desired level
- Turn off the computer but do not unplug it
- Restart the computer
If the settings hold, you've diagnosed a dead PRAM battery.