Craftsman Riding Lawnmower Won't Start?

I have a Craftsman Lawn Tracker model no. 917.28910. It is only about 4 years old. I have a problem starting it. I changed the battery and it will start on a dime. I will mow the lawn, clean it up, let is sit for a while, and try to start it up again to put it away and it won't start. It will click and sometimes if I hold the key to start a little longer than usual, it will turn over and start.

Most of the time it won't do that either. Is there something that charges the battery while it is running such as an alternator? It seems after it starts and runs, the battery drains to a point that it won't have enough juice to start up. I changed the spark plug and no help there. Checked all the wiring and nothing is loose or corroded. Any help or ideas on what to do?

By Antonio G