When the battery is taken out, the DS2781 will continue to read the battery voltage since it is still powered on. The voltage read by DS2781 will become zero now that the battery is removed. The DS2781 then would assume that the battery is fully discharged, thus clearing the ACR to zero. Under this circumstance, the battery capacity reading from DS2781 would still be zero even if the battery is plugged back in.
However, if the VDD voltage supply pin and the VIN voltage measurement pin are both connected to the battery, the DS2781 would be disconnected from power after the battery is removed. The value in ACR will be stored in EEPROM as a result. When the battery is plugged back in, as long as the change in capacity is not huge, DS2781 should be able to report an accurate reading, and function normally. Therefore, it is necessary that the battery powers the DS2781.