Assuming the "write after power-off event" theory is correct, I would be tempted to connect a battery pack of the same voltage to where C4 goes via a diode. C4 is the cap on the power rail for the micro and the eeprom. The diode will act as a switch isolating the battery from the board when the board is powered, but allow the battery to immediately take over when the power is cut. It will be .6v lower, but still enough to run the micro and eeprom.
The eeprom goes into data protection when Vcc falls below 1.4v and the micro needs 4v to operate. Of those two, the CPU is more sensitive to the cap bleeing down.
If we keep that voltage above 4v as described, we can find out if the cap is draining too fast without having a 'scope. Either it will retain its memory or it will not.
If that doesn't bring the memory back, we need to consider that the eeprom writes with every PTT or channel change event, or at a repetitious rate. It is somewhat possible that the eeprom was written too many times.
One way to see how often the eeprom is being written (and read) without a 'scope is to monitor the chip select pin. The micro should only be bringing it high to access it, so you are likely to see one of three things. It go high when you power cycle the radio, whenever you change a setting, or in a repetitious way (and we hope its not because that is pointless wear on the eeprom). The first two you can see with the meter in DC, the third may need the AC setting.
Overlay of CPU traces attached. Photoshopped the top and bottom into one.
