Harman Kardon AVR 65 looses preset settings after power failure. Why?

There is either a battery or capacitor inside your receiver that is no longer working to back up the presets when the power goes off. You can remove the cover and see if you can spot a battery (there would only be one if there is one). It would be small but it will be soldered in place so unless you are comfortable desoldering I would take it to a local repair shop. It is not expensive to repair.