In the winter it partially refills from the bottom which suggests after heavy rain when the soil is saturated the water table is higher than the bottom of the pond.
I know that dewponds on chalk were filled by rainwater and retained water because the evaporation was less than the rain input. Obviously the clay seal has failed but I wonder if the hydrostatic pressure from the water table could displace the clay and rupture it?
A plastic liner will be rather expensive and I have witness one of those being blistered from water rising underneath in a pond belonging to a denizen of this group.
I'm looking for pointers to solve the leak, attempts have been unsuccessfully made to puddle the clay again and an exploratory dig appears to show the clay is good and moist.