Going old-school, a clockwork chart recorder sort of arrangement using a cheap battery-powered (or battery-backed) clock movement would remove the need for microcontrollers etc.
All you need is a drum (if you don't mind the recording looping) or roll of paper (EG a shop till receipt reel), some sort of indicator or marking device, and mains-powered solenoid or similar to move it so that when it's powered, it marks in one place, and when the mains drops it moves to another place.
It could be easily done using a dish of sand, where the hour hand of the clock sweeps a line in the sand (like a robot zen garden project I saw somewhere), that would give you 12 hours endless recording.
Adding features like timestamps etc. is left as an exercise for the user ;)