Pat,
A lot of these comments are touching on the general question of why the batteries are dead, which may or may not be related to the refrigerator. The service tech should be measuring the current drain with the refrigerator both ON and OFF to figure out how many amps are being pulled from the batteries.
If you can find the Kill-a-Watt device, try plugging the refrigerator transfer switch into it to find out how much power the refrigerator is pulling.