I know of a few instances. I owned one for a while that had similar issues.
Did the issue persist from the 80s when the receiver was made? Failing to hold stations may indicate loss of power to the volatile memory, from a battery or supercapacitor or even just a large value capacitor failing to work properly.
If the issue existed within just years after production, I imagine a failing battery would not be the cause. Otherwise that's the first place I would look.
I have fixed a NAD receiver like this one before and worked on many digital receivers. All had batteries or high value capacitors to save the station after device is powered off.