The Simplicity Rider has a safety feature built into the seat. You must be sitting in the seat when the parking brake is released for the engine to continue running. If the engine shuts down then the safety feature is not recognizing that someone is sitting in the seat and the rider needs to be taken into a Simplicity dealer to determine the cause of the failure.
Here's a link to the Simplicity dealer locator: http://www.simplicitymfg.com/us/en/suppo...
I assume that you are sitting in the seat when the parking brake is released. If that is true you probably have a bad safety switch. I would suspect the seat switch.
I have a Simplicity Regent Riding Mower. The engine stops when the parking brake is released