I don't believe the mower is charging the battery. When installing a newly-charged battery with an external charger, I get 13.4 volts. The starter will crank the engine quickly. A week or so later, the battery will show about 12.3 volts, which should be enough to start the mower. However, the mower will start crank slowly but eventually start. Have tried a new battery-still same results-engine turns over slowly. Even if I use the pull-rope to start the engine, the starter will crank slowly even with a warm engine and mowing for at least 30 minutes. I have a new starter which works great with a fully charged battery from an external charger. It is after not mowing for at least a week, starter acts like it has a very low battery charge-it will barely turn over (sometimes it will NOT work at all-just hear the whirring sound of the Bendix.
Have tried two different batteries with the same result. When this mower was new in 2013 I never worried about an electric start. It would work all season without any problems. Took the battery out for the winter, charged it in the Spring, installed it and it worked all year.