What is the most likely cause of my battery losing it's charge over a short period of time? It seems like it does not charge while the mower is being used.
We can't give very good advise on information that " seems like ".
If you've never cleaned the battery terminals or both cable ends of both battery cables that would be a good place to start trouble shooting. A battery brush or sand paper will remove any oxide down to bare metal. A common steel brush won't hack it.
After they are clean, check the battery Voltage with the engine dead then start the engine, run to 2/3 to full throttle and check Voltage at the battery terminals again. This will take away the "seems like " factor. Report the readings back to the forum and we can give better advise from that point.