This is pure guesswork based on zero experience... and no knowledge of lawnmowers...
If your mower has an old fashioned motor-driven Generator to charge the battery - rather than an automible style alternator - then there will need to be a relay between the battery and the generator to disconnect them from one another when the motor stops - else when the engine stops the battery will be trying to turn the generator over as if it were an electric motor - and quickly become discharged.
I would look for a realay in the charging circuit and be very suspicious of it.
Good luck...
Peccavi
April 2010