Sounds like the lithium backup battery pack may be dead. Open up the case and get to the battery. Check to see if you get a 3.6 volt reading or higher. If not, the battery needs to be replaced.

After replacing the battery, reset the PMU/CUDA by pressing the reset button once for one second. Then, reset the PRAM. Yeah, I know. This will reset everything how you set it, but that's what happens.

Also, watch the power supply and rechargeable battery; make sure they're up to par.

73s 8)