I have the same problem, the reason for my clock not working is a resistor on the underside of the circuit board
failing, causing the battery not to receive a charge.
You can easily test to see if you have the same problem,
first desolder the battery making a note of the connections
(brown to + on mine), rinse off white powder on battery
under tap, next you will need to zap the battery, i use 2
fully charged AA nicad cells in holder, connect neg to neg
then spark the positive to the positive of the button cell.
Do not keep connected together for more than 2 seconds at the time, do this a few times allowing the cell
to recover between.
Take a multimeter reading to see if the cell has taken
the charge, if it has carefully resolder to clock observing
polarity. If clock starts to run then you have the same
problem as me, clock will not operate properly until
resistor is changed.