The clock should be running with so low voltage that I would not assume the battery being an issue. I have not seen a similar issue but considering how digital clocks generally work, it sounds like your crystal circuitry has a fault, or the crystal itself has failed (that usually asks for a mechanical shock, not likely on a car), perhaps one of the capacitors has soldering issues or something similar.
The clock is clearly faulty, I'm afraid the dealer option would be to change the cluster (isn't the clock part of the cluster on a W210). An electronics expert might find a low cost solution, perhaps some of those who repair instrument clusters for lost LCD segments etc.