Try disconnecting the ground wire from the battery after you finish using the mower and see if the battery still gets discharged after a week of sitting idle. If it is still getting discharged, then the battery is the problem. Otherwise, there is a slow current leak somewhere in the mower's battery charging circuit. Also, does the mower have lights that might not be turned off ?
Thanks Mike! I'll give it a try. There are no lights on the mower. The only thing I can see that requires any current is the digital hour meter. I appreciate your suggestion!