I've checked the John Deere web site and they answer this issue with "The charging system is dramatically affected by engine RPM. Even running at 10% low on RPM will make a significant reduction in charging output. Running at less than full throttle can slowly drain the battery because the charging system cannot keep up with the demands on the battery (lights, PTO clutch). At idle, the charging system has almost no output." I have already replaced the OEM battery and the new battery is following the same path of not charging. Is John Deere correct or might there be other electrical issues with the lawn tractor because when the tractor is hot from running for several hours the RIO switch doesn't work.

I had the same problem and found a broken wire under the flywheel that is connected to the charging system

Hi,
It is a full-wave system. A good static check is to check the battery at rest (nothing on) for between 12.6 - 13.2 V (usual range) and then with engine at full throttle for about 14.5 V at least. This does not check current, but is the usual first check. You may want to supplement this by carefully checking the latter with someone on the seat (someone on seat, park brake on and watch your toes/the deck.)
Peace,
Clarke