Hello,
I'm not an electronics engineer, but if you look at the diagram (
http://www.chesscomputeruk.com/Mephisto_Senator.pdf),
you can see that the battery feeds capacitors C5 to C10,
but these are the components that age the worst, by changing capacity but also by increasing their leakage current...
Page 2 indicates the current consumption of the stop mode, from 2 to 10 µA maximum: you could check this with a multimeter
the value consumed by the battery in this stop mode.
If it's over 10 µA, change the capacitors, starting with C5, which is electrolytic and has a high capacitance (and also C3).
Cordially.
2878FE54DE3E6571AB155EEFA1F81C0E751173F0