Depends on your specific 51 derivative. Some are built from EEPROM cells and you could save the last known time when you power off, IF your systems knows ahead of time when that happens (power fail with large C)
You will not be able to track time, but you might be able to track usage of your device. Time will fly by while the device is switched off, usage is "0" during off mode.
hth, Bob
as FvM mentioned a backup battery and a Real-Time-Clock would make life a lot easier though.